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Dynamical graph grammars (DGGs) are capable of modeling and simulating the dynamics of the cortical microtubule array (CMA) in plant cells by using an exact simulation algorithm derived from a master equation; however, the exact method is slow for large systems. We present preliminary work on an approximate simulation algorithm that is compatible with the DGG formalism. The approximate simulation algorithm uses a spatial decomposition of the domain at the level of the systems time-evolution operator, to gain efficiency at the cost of some reactions firing out of order, which may introduce errors. The decomposition is more coarsely partitioned by effective dimension (d= 0 to 2 or 0 to 3), to promote exact parallelism between different subdomains within a dimension, where most computing will happen, and to confine errors to the interactions between adjacent subdomains of different effective dimensions. To demonstrate these principles we implement a prototype simulator, and run three simple experiments using a DGG for testing the viability of simulating the CMA. We find evidence indicating the initial formulation of the approximate algorithm is substantially faster than the exact algorithm, and one experiment leads to network formation in the long-time behavior, whereas another leads to a long-time behavior of local alignment.

The current investigation formulated an efficient computing technique by incorporating the algorithm of Artificial Neural Network Levenberg Marquardt Method (ANNLMM) to approximate Soret and Dufour effects on Magnetohydrodynamic squeezing flow of Jeffrey fluid (MHDSFJF) in MATLAB environment. Due to its efficiency and flexibility, the applied neural network model can accurately predict the output results. In the ANNLMM, 80% of the data is used for training and 10% is set for both the testing and validation processes. The flow under consideration is mathematically formulated with the help of Navier Stokes Equations. The partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) by similarity variables. The effects of the physical parameters are discussed briefly. When the Hartmann number and Jeffrey fluid parameter increase, the concentration, temperature, and velocity profiles decreases. The temperature profile and heat transfer rate are improved by the effects of joule dissipation, Dufour numbers, and heat generation/absorption. On the other hand, as thermal radiation rises, the temperature profile decreases and the heat transfer rate increases. With an augment in Soret number, the mass transfer rate increases and the concentration profile slows down. Additionally, increasing chemical reactions, the mass transfer rate increases, but in convective chemical reactions, the contradiction is observed.

The present study performs the design of a novel Gudermannian neural networks (GNNs) for the nonlinear dynamics of prey-predator system (NDPPS). The process of GNNs is applied using the global and local search approaches named as genetic algorithm and interior-point algorithms, i.e., GNNs-GA-IPA. An error-based merit function is constructed using the NDPPS and its initial conditions and then optimized by the hybrid of GA-IPA. Six cases of the NDPPS using the variable coefficients have been presented and the correctness is observed through the overlapping of the obtained and Runge-Kutta reference results. The results of the NDPPS have been performed between 0 and 5 using the step size 0.02. The graph of absolute error are performed around 10−06 to 10−08 to check the consistency of the proposed GNNs-GA-IPA. The statistical analysis based minimum, median and semi-interquartile ranges have been performed for both predator and prey dynamics of the model. Moreover, the investigations through the statistical operators are performed to validate the reliability of the obtained outcomes based on multiple trials.

In order to reduce cross-infections during epidemics such as COVID-19, it is valuable to design a campus takeout system of intelligent self-pickup cabinets (ISPCs). This research aims to design such a system by optimizing the sites of cabinets, their capacity types, and the location–allocation scheme. In view of maximizing profits of the system, we formulate this design problem as a zero–one integer nonlinear programming model, where the demand of takeout is distance dependent and congestion dependent, rather than a fixed constant. On the basis of model property analysis, the original model is transformed into an integer linear programming problem such that it is solved by off-the-shelf solvers. By case study and sensitivity analyses, it is found that: The proposed method is valuable for providing an optimal strategy for a takeout system of ISPCs by optimizing the sites of the cabinets, the capacity types and the location–allocation strategy; With the optimal strategy derived from the proposed model and algorithm, the developed system is more applicable in the areas of intensively distributed users or the areas closer to canteens in view of creating significant effects of scale economy; For the groups of consumers with different distance-dependent or congestion-dependent sensitivities, it is suggested to implement distinct optimal strategies of building the takeout system even for those in the same service area; The takeout demand grows up with an increasing unit selling price in the developed system, rather than reduction as in an ordinary relation between the demand of products and the price. Thus, the designed self-pickup takeout system seems more applicable to be adopted for the high-quality takeout. [ABSTRACT FROM AUTHOR]

As a novel biological computing device, the Spiking Neural P system (SNPS) has powerful computing potential. The application of SNPS in the field of arithmetic operation has been a hot research topic in recent years. Researchers have proposed methods and systems for implementing basic arithmetic operations using SNPS. This paper studies four basic arithmetic operations, improves the parallelization of addition and multiplication methods, and designs more effective natural number addition and multiplication SNPS, as well as SNPS for subtraction and for division of natural numbers based on multiple subtractions. The effectiveness of the proposed SNPS is verified by example. Compared with the same kind of SNPS, for the addition operation the number of neurons used in our system is reduced by 50% and the time overhead is reduced by 33%, while for the multiplication operation the number of neurons is reduced by 40%. [ABSTRACT FROM AUTHOR]

In this study, the design of a computational heuristic based on the nonlinear Liénard model is presented using the efficiency of artificial neural networks (ANNs) along with the hybridization procedures of global and local search approaches. The global search genetic algorithm (GA) and local search sequential quadratic programming scheme (SQPS) are implemented to solve the nonlinear Liénard model. An objective function using the differential model and boundary conditions is designed and optimized by the hybrid computing strength of the GA-SQPS. The motivation of the ANN procedures along with GA-SQPS comes to present reliable, feasible and precise frameworks to tackle stiff and highly nonlinear differentialmodels. The designed procedures of ANNs along with GA-SQPS are applied for three highly nonlinear differential models. The achieved numerical outcomes on multiple trials using the designed procedures are compared to authenticate the correctness, viability and efficacy. Moreover, statistical performances based on different measures are also provided to check the reliability of the ANN along with GASQPS. [ABSTRACT FROM AUTHOR]

The present study articulates a novel heuristic computing design with artificial intelligence algorithm by manipulating the models with Feed forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of Genetic algorithms (GA) combined with rapid local convergence of Active-set method (ASM), i.e., FF-GNN-GAASM for solving the second kind of Three-point singular boundary value problems (TPS-BVPs). The proposed FF-GNN-GAASM intelligent computing solver integrated into the hidden layer structure of FF-GNN systems of differential operatives of the second kind of STP-BVPs, which are linked to form the error based Merit function (MF). The MF is optimized with the hybrid-combined heuristics of GAASM. The stimulation for presenting this research work comes from the objective to introduce a reliable framework that associates the operational features of NNs to challenge with such inspiring models. Three different measures of the second kind of TPS-BVPs is applied to assess the robustness, correctness and usefulness of the designed FF-GNN-GAASM. Statistical evaluations through the performance of FF-GNN-GAASM is validated via consistent stability, accuracy and convergence. [ABSTRACT FROM AUTHOR]

The present communication examines the unsteady-two-dimensional (2-D) squeezing flow of magnetohydrodynamic (MHD) Jeffrey fluid between two parallel plates (HT2DUSMHDJF). In its own plane, the bottom channel plate is extended while the upper plate squeezes towards the lower plate. The complete structure is takan is a rotating frame. Cattaneo-Christov heat flux model (CCHFM) is forced to explore the features of heat transfer. Distinct the conventional position, Instead of the Fourier heat conduction law, the heat flux is implemented by the Cattaneo-Christov theory. The resultant systems are computed through Artificial Neural Network (ANN). The behaviors of a number of relevant parameters are analyzed through graphs and numerical data. The velocity profile increases for Deborah number β and squeezing parameter sq and decreases for rotation, magnetic and relaxation time parameter ω , M, and λ 1 respectively. Also the Skin friction coefficient decreases for λ 1 and Sq and increases for high value of Deborah numbers β , ω and M. [ABSTRACT FROM AUTHOR]

ABSTRAK Ilmu tentang gelombang adalah salah satu dasar untukmengembangkan peralatan yang kita gunakan dewasa ini, mulai dari smartphone, televisi dan perlatan masakpun ada yang menggunakan gelombang. Pembelajaran gelombang ini sudah didapatkan semenjak berada di bangku sekolah dasar sampai sekolah menengah atas. Akan tetapi persamaan gelombang sangatlah sulit untuk dipahami, karena rumusan matematisnya yang sangat kompleks. Komputer merupakan suatu perangkat modern yang memiliki banyak kelebihan, antara lain kemampuan numeriknya yang bagus, bisa memvisualisasikan data dalam bentuk grafik dan pengoperasiannya sangat mudah. Tujuan dari penelitian ini untuk memvisualisasikan grafik perlayangan gelombang dengan menggunakan excel dan matlab Metode penelitian yang digunakan adalah metode kuantitatif, dilakukan dua tahapan penelitian dan dilaksanakan di laboratorium fisika Universitas Semarang. Peneliti mensimulasikan dari variabel amplitudo dan frekuensi gelombang, sehingga diperoleh visualisasi grafik perlayangan gelombang. Grafik yang dihasilkan dengan menggunakan Excel dan Matlab sama. Tetapi dengan menggunakan Matlab lebih praktis karena grafiknya hanya dihasilkan dalam satu pandangan tiga dimensi saja, sedangkan dengan menggunakan Excel hasil grafik yang diperoleh terbagi dalam bentuk dua pandangan yaitu dua dimensi. Kata kunci : perlayangan gelombang; komputasi numerik; matlab ABSTRACT The science of waves is one of the basics for developing the equipment we use today, from smartphones, televisions and cooking utensils, some use waves. This wave of learning has been obtained since elementary school to high school. However, the wave equation is very difficult to understand, because the mathematical formulation is very complex. The computer is a modern device that has many advantages, including good numerical capabilities, being able to visualize data in graphical form and operating very easily. The purpose of this research is to visualize the wave gliding graph using excel and matlab. The research method used is a quantitative method, carried out in two stages of research and carried out in the physics laboratory of the University of Semarang. The researcher simulates the amplitude and frequency of the waves, so that a graphic visualization of the wave gliding is obtained. Graphs generated using Excel and Matlab are the same. But using Matlab is more practical because the graph is only in one 3-dimensional view, while using Excel the graph is divided into two views in 2 dimensions. Keywords: wave gliding; numerical computing; matlab

The aim of the current study is to present the numerical solutions of a nonlinear second-order coupled Emden–Fowler equation by developing a neuro-swarming-based computing intelligent solver. The feedforward artificial neural networks (ANNs) are used for modelling, and optimization is carried out by the local/global search competences of particle swarm optimization (PSO) aided with capability of interior-point method (IPM), i.e., ANNs-PSO-IPM. In ANNs-PSO-IPM, a mean square error-based objective function is designed for nonlinear second-order coupled Emden–Fowler (EF) equations and then optimized using the combination of PSO-IPM. The inspiration to present the ANNs-PSO-IPM comes with a motive to depict a viable, detailed and consistent framework to tackle with such stiff/nonlinear second-order coupled EF system. The ANNs-PSO-IP scheme is verified for different examples of the second-order nonlinear-coupled EF equations. The achieved numerical outcomes for single as well as multiple trials of ANNs-PSO-IPM are incorporated to validate the reliability, viability and accuracy. [ABSTRACT FROM AUTHOR]

The objective of the presented communication is to examine and analyze the solutions of nonlinear multi-singular fifth-order Lane–Emden (LE) system for different scenarios by variation of shape factors settled on the equivalent design of the LE equations. The neuro-evolution based stochastic computing is explored for the numerical measures using the artificial neural networks (ANNs) models for the appropriate continuous mapping, while the learning of decision variables is conducted using the integrated meta-heuristic global search of genetic algorithms (GA) hybrid with the local search efficiency of active-set (AS) i.e., ANN-GA-AS scheme. The numerical approach ANN-GA-AS is applied efficiently for the fifth kind of nonlinear LE model and statistical calculations further validate the accuracy, robustness as well as convergence. [ABSTRACT FROM AUTHOR]

In the present study, design of intelligent numerical computing through backpropagated neural networks (BNNs) is presented for numerical treatment of the fluid mechanics problems governing the dynamics of magnetohydrodynamic fluidic model (MHD-NFM) past a stretching surface embedded in porous medium along with imposed heat source/sink and variable viscosity. The original system model MHD-NFM in terms of PDEs is converted to nonlinear ODEs by introducing the similarity transformations. A reference dataset for BNNs approach is generated with Adams numerical solver for different scenarios of MHD-NFM by variation of parameter of viscosity, parameter of heat source and sink, parameter of permeability, magnetic field parameter, and Prandtl number. To calculate the approximate solution for MHD-NFM for different scenarios, the training, testing, and validation processes are conducted in parallel to adapt neural networks by reducing the mean square error (MSE) function through Levenberg–Marquardt backpropagation. The comparative studies and performance analyses through outcomes of MSE, error histograms, correlation and regression demonstrate the effectiveness of proposed BNNs methodology. [ABSTRACT FROM AUTHOR]

As a novel biological computing device, the Spiking Neural P system (SNPS) has powerful computing potential. The application of SNPS in the field of arithmetic operation has been a hot research topic in recent years. Researchers have proposed methods and systems for implementing basic arithmetic operations using SNPS. This paper studies four basic arithmetic operations, improves the parallelization of addition and multiplication methods, and designs more effective natural number addition and multiplication SNPS, as well as SNPS for subtraction and for division of natural numbers based on multiple subtractions. The effectiveness of the proposed SNPS is verified by example. Compared with the same kind of SNPS, for the addition operation the number of neurons used in our system is reduced by 50% and the time overhead is reduced by 33%, while for the multiplication operation the number of neurons is reduced by 40%.

The present study is related to design a stochastic framework for the numerical treatment of the Van der Pol heartbeat model (VP-HBM) using the feedforward artificial neural networks (ANNs) under the optimization of particle swarm optimization (PSO) hybridized with the active-set algorithm (ASA), i.e., ANNs-PSO-ASA. The global search PSO scheme and local refinement of ASA are used as an optimization procedure in this study. An error-based merit function is defined using the differential VP-HBM form as well as the initial conditions. The optimization of the merit function is accomplished using the hybrid computing performances of PSO-ASA. The designed performance of ANNs-PSO-ASA is implemented for the numerical treatment of the VP-HBM dynamics by fluctuating the pulse shape adjustment terms, external forcing factor and damping coefficient with fixed ventricular contraction period. To perform the correctness of the present scheme, the obtained numerical results through the designed ANN-PSO-ASA will be compared with the Adams numerical method. The statistical investigations with larger dataset are provided using the "mean absolute deviation", "Theil's inequality coefficient" and "variance account for" operators to perform the applicability, reliability, and effectiveness of the designed ANNs-PSO-ASA scheme for solving the VP-HBM. [ABSTRACT FROM AUTHOR]

A control problem of the robot’s end-effector movement along a predefined trajectory is considered. The aim is to reduce the work against resistance forces and improve the comfortability of the motion. The integral of kinetic energy and weighted inertia forces for the whole period of motion is introduced as a cost functional. By applying variational methods, the problem is reduced to a system of quasilinear ordinary differential equations of the fourth order. Numerical examples of solving the problem for movement along straight, circular and elliptical trajectories are presented. For the sake of clarity, the problem is studied for a specific kind of a 3D printer in the 2DoF approximation. However, in the case of negligible masses of moving elements compared the mass of an end-effector, the solution is universal, i.e., it remains the same for given trajectories.

In the present study, modeling of intelligent numerical computing through Levenberg–Marquardt back propagation-based supervised neural network (LMB-SNN) is incorporated to analyze the magnetohydrodynamic flow of a third grade fluid for wire coating analysis (MHD-TGFWCA). The original mathematical formulations in terms of partial differential equations for MHD-TGFWCA are converted into a system of ordinary differential equations through dimensionless parameters and a suitable transformation mechanism. A reference dataset for the LMB-SNNs scheme is created with Adam's numerical technique for various scenarios by variation of different physical quantities such as third grade fluid parameter, magnetic parameter, and the velocity ratio parameter. To compute the approximate solution for MHD-TGFWCA in terms of various scenarios, the training, testing, and validation operations are carried out in parallel to adjust neural networks by developing the mean square error function (MSEF) through Levenberg–Marquardt back-propagation. The comparative analyses and performance studies through outputs of MSEF, regression illustrations, and error histograms validate the effectiveness of the suggested solver LMB-SNNs. The method's precision is verified by the closest numerical outputs of both built and dataset values with similar levels 10 - 5 to 10 - 9 . [ABSTRACT FROM AUTHOR]

In physical science, nonlinear singular Lane–Emden and pantograph delay differential equations (LE–PDDEs) have abundant applications and thus are of great interest for the researchers. The presented investigation is related to the development of a new application of intelligent computing for the solution of the LE–PDDEs-based system introduced recently by merging the essence of delay differential equation of Pantograph type and standard second-order Lane–Emden equation. Intelligent computing is exploited through Levenberg–Marquardt backpropagation networks (LMBNs) and Bayesian regularization backpropagation networks (BRBNs) to provide the solutions to nonlinear second-order LE–PDDEs. The performance of design LMBNs and BRBNs is substantiated on three different case studies through comparative analysis from known exact/explicit solutions. The correctness of the designed solvers for LE–PDDEs is further certified by accomplishing through assessment on error histograms, regression measures and index of mean squared error. [ABSTRACT FROM AUTHOR]

The study describes a framework based on stochastic trees and Monte Carlo methods able to compute price and greeks of a European-American Knock-Out deal (EAKO). EAKOs are contracts traded over-the-counter (OTC) and measuring their fairvalues require advanced mathematical techniques. In the first part of the paper the pay-off of the structured product is explained, in the second part the mathematical models are described and in the last part the techniques are implemented and validated in Matlab environment.

In this research paper, an innovative bio-inspired algorithm based on evolutionary cubic splines method (CSM) has been utilized to estimate the numerical results of nonlinear ordinary differential equation Painlevé-I. The computational mechanism is used to support the proposed technique CSM and optimize the obtained results with global search technique genetic algorithms (GAs) hybridized with sequential quadratic programming (SQP) for quick refinement. Painlevé-I is solved by the proposed technique CSM-GASQP. In this process, variation of splines is implemented for various scenarios. The CSM-GASQP produces an interpolated function that is continuous upto its second derivative. Also, splines proved to be stable than a single polynomial fitted to all points, and reduce wiggles between the tabulated points. This method provides a reliable and excellent procedure for adaptation of unknown coefficients of splines by searching globally exploiting the performance of GA-SQP algorithms. The convergence, exactness and accuracy of the proposed scheme are examined through the statistical analysis for the several independent runs. [ABSTRACT FROM AUTHOR]

Monte Carlo simulation (MCS) is useful for verifying analytical derivations and studying complex systems on an empirical basis. Although MCS is straightforward and does not require a priori knowledge of the sampled probability measures (PMs), it consumes a tremendous amount of computational resource and suffers from slow simulation procedures for sophisticated systems. To mitigate this drawback of MCS, we make full use of the monotone property and the logarithmic presentation convention of PMs in regard to power related metrics (PRMs) in communications science and propose an easy-to-implement interrupt mechanism to accelerate MCS for estimating PMs. To facilitate the programming on different platforms and provide a solid theoretical foundation, we present a generic implementation framework suited for estimating PMs with certain properties by MCS and analyze the underlying theory of the interrupt mechanism. In particular, we apply the de Moivre-Laplace theorem and analytic continuation to prove the asymptotic consistency under the indirect setup of MCS. We also design a hypothesis test for studying the proposed mechanism on a statistical basis. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this work is to develop a high‐performance, flexible, and easy‐to‐use MRI reconstruction framework using the scientific programming language Julia. Methods: Julia is a modern, general purpose programming language with strong features in the area of signal/image processing and numerical computing. It has a high‐level syntax but still generates efficient machine code that is usually as fast as comparable C/C++ applications. In addition to the language features itself, Julia has a sophisticated package management system that makes proper modularization of functionality across different packages feasible. Our developed MRI reconstruction framework MRIReco.jl can therefore reuse existing functionality from other Julia packages and concentrate on the MRI‐related parts. This includes common imaging operators and support for MRI raw data formats. Results: MRIReco.jl is a simple to use framework with a high degree of accessibility. While providing a simple‐to‐use interface, many of its components can easily be extended and customized. The performance of MRIReco.jl is compared to the Berkeley Advanced Reconstruction Toolbox (BART) and we show that the Julia framework achieves comparable reconstruction speed as the popular C/C++ library. Conclusions: Modern programming languages can bridge the gap between high performance and accessible implementations. MRIReco.jl leverages this fact and contributes a promising environment for future algorithmic development in MRI reconstruction. [ABSTRACT FROM AUTHOR]

This research work is to design a neural-swarming heuristic procedure for numerical investigations of Singular Multi-Pantograph Delay Differential (SMP-DD) equation by applying the function approximation aptitude of Artificial Neural Networks (ANNs) optimized efficient swarming mechanism based on Particle Swarm Optimization (PSO) integrated with convex optimization with Active Set (AS) algorithm for rapid refinements, named as ANN-PSO-AS. A merit function (MF) on mean squared error sense is designed by using the differential ANN models and boundary condition. The optimization of this MF is executed with the global PSO and local search AS approaches. The planned ANN-PSO-AS approach is instigated for three different SMP-DD model-based equations. The assessment with available standard results relieved the effectiveness, robustness and precision that is further authenticated through statistical investigations of Variance Account For, Root Mean Squared Error, Semi-Interquartile Range and Theil's inequality coefficient performances. [ABSTRACT FROM AUTHOR]

A control problem of the robot's end-effector movement along a predefined trajectory is considered. The aim is to reduce the work against resistance forces and improve the comfortability of the motion. The integral of kinetic energy and weighted inertia forces for the whole period of motion is introduced as a cost functional. By applying variational methods, the problem is reduced to a system of quasilinear ordinary differential equations of the fourth order. Numerical examples of solving the problem for movement along straight, circular and elliptical trajectories are presented. For the sake of clarity, the problem is studied for a specific kind of a 3D printer in the 2DoF approximation. However, in the case of negligible masses of moving elements compared the mass of an end-effector, the solution is universal, i.e., it remains the same for given trajectories. [ABSTRACT FROM AUTHOR]

The current study develops a novel application of numerical computing paradigm to inspect the cumulative effects of both electric and magnetic field on a micropolar nanofluid bounded by two parallel plates in a rotating system by using Adams and Explicit Runge–Kutta (RK) solvers. The steady state micropolar nanofluidics flow has been considered between parallel plates under the Hall current effect. The conventional expressions for the governing flow in terms of system of ODEs are engaged. Adams and Explicit RK-based numerical solvers have been exploited for approximate solution of the system dynamics. Accuracy, convergence and stability analyses of both numerical schemes established their correctness. The impact of the Sherwood number on the concentration profile, Nusselt number and coefficient of skin friction on temperature and velocity profiles, respectively, have been analyzed numerically along with thermophoresis investigation, rotation, Hall current and Brownian motion of micropolar nanofluid. The effect of physical quantities including viscosity, magnetic, rotating, coupling, Brownian motion, thermophoretic and micropolar fluid parameters as well as Prandtl and Schmidt numbers has been presented. [ABSTRACT FROM AUTHOR]

The present study performs the design of a novel Gudermannian neural networks (GNNs) for the nonlinear dynamics of prey-predator system (NDPPS). The process of GNNs is applied using the global and local search approaches named as genetic algorithm and interior-point algorithms, i.e., GNNs-GA-IPA. An error-based merit function is constructed using the NDPPS and its initial conditions and then optimized by the hybrid of GA-IPA. Six cases of the NDPPS using the variable coefficients have been presented and the correctness is observed through the overlapping of the obtained and Runge-Kutta reference results. The results of the NDPPS have been performed between 0 and 5 using the step size 0.02. The graph of absolute error are performed around 10 -06 to 10 -08 to check the consistency of the proposed GNNs-GA-IPA. The statistical analysis based minimum, median and semi-interquartile ranges have been performed for both predator and prey dynamics of the model. Moreover, the investigations through the statistical operators are performed to validate the reliability of the obtained outcomes based on multiple trials., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 Published by Elsevier Ltd.)

In the current study, the nonlinear radiative heat transfer effects due to solar radiation in magneto-hydrodynamic (MHD) nanofluidic problem are analyzed effectively by novel application of numerical computing by Adams predictor–corrector and explicit backward difference solvers. The governing relations of PDEs for the model are transformed into the system of ODEs, and numerical solvers are applied to the transformed system to study the effect of radiation parameter along with thermophoresis parameter, Brownian motion parameter, magnetic field parameter, Lewis number, Prandtl number, Eckert number and Biot number on velocity, temperature and nanoparticle concentration profiles. The comparative study of both solvers is provided in sufficient number of graphical and numerical illustrations to prove the worth in terms of accuracy, robustness and stability. [ABSTRACT FROM AUTHOR]

The designed fractional order Stuxnet, the virus model, is analyzed to investigate the spread of the virus in the regime of isolated industrial networks environment by bridging the air-gap between the traditional and the critical control network infrastructures. Removable storage devices are commonly used to exploit the vulnerability of individual nodes, as well as the associated networks, by transferring data and viruses in the isolated industrial control system. A mathematical model of an arbitrary order system is constructed and analyzed numerically to depict the control mechanism. A local and global stability analysis of the system is performed on the equilibrium points derived for the value of α = 1. To understand the depth of fractional model behavior, numerical simulations are carried out for the distinct order of the fractional derivative system, and the results show that fractional order models provide rich dynamics by means of fast transient and super-slow evolution of the model’s steady-state behavior, which are seldom perceived in integer-order counterparts.

The current study aims to design an integrated numerical computing-based scheme by applying the Levenberg–Marquardt backpropagation (LMB) neural network to solve the nonlinear susceptible (S), infected (I) and recovered (R) (SIR) system of differential equations, representing the spreading of infection along with its treatment. The solutions of both the categories of spreading infection and its treatment are presented by taking six different cases of SIR models using the designed LMB neural network. A reference dataset of the designed LMB neural network is established with the Adam numerical scheme for each case of the spreading infection and its treatment. The approximate outcomes of the SIR system based on the spreading infection and its treatment are presented in the training, authentication and testing procedures to adapt the neural network by reducing the mean square error (MSE) function using the LMB. Studies based on the proportional performance and inquiries based on correlation, error histograms, regression and MSE results establish the efficiency, correctness and effectiveness of the proposed LMB neural network scheme.

To more realistically describe the operation of an eddy current brake under intensive impact load, a magnetic-thermal bidirectional coupling model of the eddy current brake is established considering the existence of temperature. The variation of material and convective heat transfer coefficient with temperature are considered in the model. The iterative method is used to decouple the model. Through the analysis of the numerical simulation results, the temperature distribution and transmission of the brake during operation are obtained. By comparison, it is found that the calculated braking force of the magneto-thermal coupling model is lower than the calculated value without considering the temperature field due to the influence of temperature. And the higher the temperature, the greater the decrease. [ABSTRACT FROM AUTHOR]

A differential evolution based methodology is introduced for the solution of elliptic partial differential equations (PDEs) with Dirichlet and/or Neumann boundary conditions. The solutions evolve over bounded domains throughout the interior nodes by minimization of nodal deviations among the population. The elliptic PDEs are replaced by the corresponding system of finite difference approximation, yielding an expression for nodal residues. The global residue is declared as the root-mean-square value of the nodal residues and taken as the cost function. The standard differential evolution is then used for the solution of elliptic PDEs by conversion to a minimization problem of the global residue. A set of benchmark problems consisting of both linear and nonlinear elliptic PDEs has been considered for validation, proving the effectiveness of the proposed algorithm. To demonstrate its robustness, sensitivity analysis has been carried out for various differential evolution operators and parameters. Comparison of the differential evolution based computed nodal values with the corresponding data obtained using the exact analytical expressions shows the accuracy and convergence of the proposed methodology. [ABSTRACT FROM AUTHOR]

Automating computational workflows leads to more reproducible research. automan assembles a suite of long-running computations, deploys them on your computational resources, and produces final plots from output data, all with a single command. [ABSTRACT FROM AUTHOR]

In this study, numerical treatment is performed to study the dynamical analysis of hydro-magnetic nanofluids problem for heat and mass transfer of an unsteady nanofluid flow between parallel plates by exploiting the strength of Adams and explicit Runge-Kutta method. Original PDEs of the model are transformed to equivalent system of ODEs by utilizing the similarity transformations. Numerical and graphical illustrations prove the validity of the proposed methods for number of scenarios of the system by considering different physical quantities such as the squeeze number, Nusselt number, Schmidt number, Hartmann number, thermophoretic parameter, Brownian motion parameter, and Eckert number. [ABSTRACT FROM AUTHOR]

The paper presents a numerical energy harvesting model for sensor nodes, SIVEH (Simulator I–V for EH), based on I–V hardware tracking. I–V tracking is demonstrated to be more accurate than traditional energy modeling techniques when some of the components present different power dissipation at either different operating voltages or drawn currents. SIVEH numerical computing allows fast simulation of long periods of time—days, weeks, months or years—using real solar radiation curves. Moreover, SIVEH modeling has been enhanced with sleep time rate dynamic adjustment, while seeking energy-neutral operation. This paper presents the model description, a functional verification and a critical comparison with the classic energy approach.

The design of integrated intelligent computing solver with Morlet wavelet neural networks (MW-NNs) is presented for solving the mathematical predator–prey model by exploiting the strength of MW-NNs modeling, optimization ability of global search with genetic algorithms (GAs) and rapid local search eminence of sequential quadratic programming (SQP), i.e., MW-NNs-GA-SQP. The proposed MW-NNs-GA-SQP scheme is used to analyze the predator–prey dynamics for six different variables coefficient values. The validation, correctness and reliability of the presented MW-NNs-GA-SQP technique is attained through the consistent matched outcomes with the reference Adams numerical results. Moreover, statistics investigations have been accomplished to verify the precision and accuracy of the outcomes with proposed MW-NNs-GA-SQP solver via the performances of Theil's inequality coefficient, Nash Sutcliffe efficiency and mean absolute error. • The design of integrated intelligent computing solver with Morlet wavelet neural network (MW-NN) is presented for solving the mathematical predator–prey model. • We use the strength of MN-NN modeling, optimization ability of global search with genetic algorithms (GAs) and rapid local search eminence of sequential quadratic programming (SQP), i.e., MW-NN-GA-SQP. • The proposed MW-NN-GA-SQP scheme is used to analyze the predator–prey dynamics for six different variables coefficient values. • The validation, correctness and reliability of the presented MWNN-GA-SQP technique is attained through the consistent matched outcomes with the reference Adams numerical results. • Statistics investigations have been accomplished to verify the precision and accuracy of the outcomes with proposed MW-NN-GA-SQP solver via the performances of Theil's inequality coefficient, Nash Sutcliffe efficiency and mean absolute error. [ABSTRACT FROM AUTHOR]

MATLAB/Simulink is a popular toolset for developing embedded software. The main target of the toolset is numerical computing applications and the tools offer a rich language for manipulating matrices. This paper presents an approach to automatic, modular, contract-based verification of programs written in a subset of the MATLAB programming language. We focus on efficient handling of the built-in matrix manipulation functions commonly used in MATLAB. We restrict ourselves to the subset of MATLAB suitable for code generation, which means matrix types and shapes can be determined statically. We present an approach to static type and shape inference for matrices that is more strict than MATLAB, but aids verification. The type and shape information is then used in the verification. From the programs and contracts we generate verification conditions that are discharged with an off-the-shelf SMT solver. We discuss two approaches to encode matrix functions and evaluate them on a number of examples. We also investigate the use of k-induction to decrease the need for user annotations. We found our approach to be efficient for programs that manipulate relatively small matrices, which are common in embedded applications. [ABSTRACT FROM AUTHOR]