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In this paper, the differential transformation method (DTM) is employed to find the semi-analytical solutions of SIS and SI epidemic models for constant population. Firstly, the theoretical background of DTM is studied and followed by constructing the solutions of SIS and SI epidemic models. Furthermore, the convergence analysis of DTM is proven by proposing two theorems. Finally, numerical computations are made and compared with the exact solutions. From the numerical results, the solutions produced by DTM approach the exact solutions which agreed with the proposed theorems. It can be seen that the DTM is an alternative technique to be considered in solving many practical problems involving differential equations. [ABSTRACT FROM AUTHOR]

Semi-analytical studies for the porosity action of a hollow sphere made of functionally graded piezoelectric material are presented. A semi-analytical technique for radial displacement is presented. A combination of internal and external pressures, temperature distribution, uniform hygrothermal distribution, and an electric potential variation has been discussed between the inner and outer surfaces of the sphere. The material physical properties for the present porous hollow sphere are varying through the thickness due to the power functions of the radius. Numerical outcomes are validated for radial displacement, electric potential, and stresses for the perfect and porous functionally graded hollow sphere. The effect of different mechanical, piezoelectric, and hygrothermal are investigated. [ABSTRACT FROM AUTHOR]

Modelling the vibrational response of railway tracks is a mandatory step to predict rolling noise. This article proposes a model based on the semi-analytical finite element method (SAFE) taking into account the three main characteristics of railway tracks: infinite length in the longitudinal direction, deformable cross-section, and periodic track support. Although this approach is ideally suited to predict rail vibrations, numerical instabilities undermine its reliability at low frequencies. Consequently, a new approach using the second-order Arnoldi reduction (SOAR) is used, which allows to provide the required numerical stability. Lastly, numerical results are compared with classical railway track behaviours described in the literature, as well as experimental data and 3D finite element simulations. [ABSTRACT FROM AUTHOR]

We construct a Heston-type stochastic volatility model with a Markov switching regime to price a plain-vanilla stock option. A semi-analytic solution, which contains a matrix ODE is obtained and numerically calculated. Our model is flexible enough to provide a wide variety of volatility surfaces for the same volatility level but different regimes. © 2015 Wiley Periodicals, Inc. Jrl Fut Mark 36:902-919, 2016 [ABSTRACT FROM AUTHOR]

Temperature span, cooling power, work, and efficiency are key performance metrics describing active magnetic regenerators used as refrigerators. Numerical methods to calculate these parameters efficiently and accurately are needed. This paper proposes a set of semi-analytic relationships to determine cooling power and magnetic work as a function of temperature span, regenerator characteristics, operating conditions, and magnetic field waveform. Appropriate effective values for magnetocaloric effect and specific heat are defined. Semi-analytic predictions for cooling power and work are validated against experimental data for room-temperature tests as well as a more complex numerical model describing magnetic work. The semi-analytic approach is found to predict performance well over the range of operating conditions considered. [ABSTRACT FROM AUTHOR]

Abstract: We study a system with bimolecular irreversible kinetic reaction where the underlying transport of reactants is governed by diffusion, and the local reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion–reaction equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies. [Copyright &y& Elsevier]

In this study, an effective modification of the semi-analytic inversion method is presented. The semi-analytic inversion method is developed to solve an inverse coefficient problem arising in materials science instead of the parametrization method as a different and stronger method. The inverse coefficient problem is related to reconstruction of the unknown coefficient,, from the nonlinear equation,. The semi-analytic inversion method has some advantages. The first distinguishable feature of this method is that it uses only a few measured output data to determine the whole unknown curve, whereas the parametrization algorithm uses many measured output data for the determination of only some part of the unknown curve. The second distinguishable feature of this method is its well-posedness. In the semi-analytic inversion method, the algorithm for determination of the yield stress, which is one of the main unknowns of the inverse problem, is very complicated. That is why we need to modify this algorithm. The demonstrated numerical results for different engineering materials also show that the modified semi-analytic inversion method allows us to determine the elastoplastic parameters of a kind of engineering materials with high accuracy, even various noise levels. [ABSTRACT FROM AUTHOR]

Abstract: The classical Blasius flow and its variation, Sakiadis flow, are investigated by the fixed point method (FPM), and the semi-analytical solutions are obtained. Different from early perturbation series solutions, the present semi-analytical solutions are valid in the whole region without using matching procedure. Moreover, these solutions can correctly provide the asymptotic property of the governing equations. The comparison of the present results with numerical results is carried out, which reveals that FPM is a convenient and effective tool for nonlinear problems. [Copyright &y& Elsevier]

New high-precision, semianalytical and numerical solutions to the problem of the rotational motion of the Moon are obtained, for use in the long 418.9-year time frame. The dynamics of the rotational motion of the Moon is studied numerically using the Rodrigues-Hamilton parameters, relative to the fixed ecliptic for the epoch J2000. The results of the numerical solution to the problem under study are compared with a compiled semianalytical theory of Moon rotation (SMR). The initial conditions for the numerical integration have been taken from the SMR. The comparative discrepancies derived from the comparison between the numerical solutions and the SMR do not exceed 1.5″ on the time-scale of 418.9 yr. The investigation of the comparative discrepancies between the numerical and semianalytical solutions is performed using the least squares and spectral analysis methods in the Newtonian case. All the periodic terms describing the behavior of the comparative discrepancies are interpreted as the corrections to the semianalytical SMR theory. As a result, the series are constructed to describe the rotation of the Moon (MRS2010) in the time interval under study. The numerical solution for the Moon's rotation has been obtained anew, with new initial conditions calculated using MRS2010. The discrepancies between the new numerical solution and MRS2010 do not exceed 20 arc milliseconds on the time-scale of 418.9 years. The results of the comparison suggest that that the MRS2010 series describe the rotation of the Moon more correctly than the SMR series. [ABSTRACT FROM AUTHOR]

A faster and accurate semianalytical formulation with a robust optimization solution for estimating the splice loss of graded-index fibers has been proposed. The semianalytical optimization of modal parameters has been carried out by Nelder-Mead method of nonlinear unconstrained minimization suitable for functions which are uncertain, noisy, or even discontinuous. Instead of normally used Gaussian function, as the trial field for the fundamental mode of graded-index optical fiber a novel sinc function with exponentially and R-3/2 (R is the normalized radius of the optical fiber) decaying trailing edge has been used. Due to inclusion of three parameters in the optimization of fundamental modal solution and application of an efficient optimization technique with simple analytical expressions for various modal parameters, the results are found to be accurate and computationally easier to find than the standard numerical method solution. [ABSTRACT FROM AUTHOR]

Abstract: Ship collisions are increasingly simulated with numerical methods predicting the structural damage, respectively the ships'' safety, in such accidental event. The latest analyses techniques can take the non-linear structural behaviour and the motions of the colliding vessels into account, however using time-consuming numerical models. Hence, a single dynamic collision can be analysed with a fair degree of accuracy, but at high computational cost. Therefore, this article presents a combined numerical and analytical procedure to assess ship collision damage with significantly lower computational cost. Numerical quasi-static collision simulations estimate the non-linear structural behaviour for a given vessel colliding at selected vertical locations. This provides the force versus penetration curves, which thus depends on the structural arrangement at the striking location. Hence, the semi-analytical collision analysis is calibrated based on these structural resistance curves in order to estimate the change in available energy for structural deformation considering different longitudinal striking locations and angles. As a result, the collision damage, respectively penetration depth and length, can be estimated for vessels of different dimensions and mass ratio''s subjected to various collision situations if the presented procedure is applied. [Copyright &y& Elsevier]

Abstract: Different preconditioning techniques for the iterative method MinRes as solver for the Discrete Sources Method (DSM) are presented. This semi-analytical method is used for light scattering computations by particles in the Mie scattering regime. Its numerical schema includes a linear least-squares problem commonly solved using the QR decomposition method. This could be the subject of numerical difficulties and instabilities for very large particles or particles with extreme geometry. In these cases, we showed that iterative methods with preconditioning techniques can provide a satisfying solution. In our previous paper, we studied four different iterative solvers (RGMRES, BiCGStab, BiCGStab(l), and MinRes) considering the performance and the accuracy of a solution. Here, we study several preconditioning techniques for the MinRes method for a variety of oblate and prolate spheroidal particles of different size and geometrical aspect ratio. Using preconditioning techniques we highly accelerated the iterative process especially for particles with a higher aspect ratio. [Copyright &y& Elsevier]

Using a semianalytical solution to the problem of wave excitation in an elastically supported one-dimensional waveguide with a system of point obstacles, we analyze the relation between the observed effects of blocking-transmission and the discrete spectrum point distribution in the complex frequency plane. We check the assumption, stemming from earlier numerical analysis for two-dimensional elastic waveguides with extended obstacles, on whether the occurrence of transmission frequencies in the blocking range is related to the presence of close-to-the-real-axis points of a discrete spectrum. The number of such spectral points increases in proportion to the number of obstacles, giving in the limit continuous transmission bands described by the Bloch-Floquet theory for infinite periodic structures. [ABSTRACT FROM AUTHOR]

In this paper the variational iteration method is used to compute the solution for the linear, variable coefficient, fractional derivative and multi space telegraph equations. The method constructs a convergent sequence of functions, to approximate the exact solution with a few number of iterations without discretization. Numerical results and comparison with exact solutions are given for some examples in order to show its applicability and efficiency. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a semi-analytic approach to the solution of the quadruple Huygens-Fresnel integral which is used to calculate the average receiver intensity of a source beam after it has propagated in a turbulent atmosphere. Our approach is based on a self-designed MATLAB function that reduces a quadruple integral to a single one by sequential operations using a form that is readily available from tables. In this manner exact numerical evaluations are obtained, whilst lengthy hand derivations are avoided. Additionally, the computation time of the new approach is not much different from that of the complete analytic solution. Two application examples are cited, also establishing agreement with our previously published results. [ABSTRACT FROM AUTHOR]

In this article, we present a two-dimentional (2D) solute transport model using streamline simulation and semi-analytical solutions of one-dimensional (1D) transport equation. We validated the accuracy of the developed model by comparing three simulation results of contaminant transport using an analytical, a semi-analytical, and an upwind finite-difference solution of 1D transport equation. We also show how to apply the developed model to simulate solute transport with complex boundary conditions, such as the first-order degraded source condition and the Cauchy boundary condition. For an advection-dominant flow, we can clearly see the differences of plume spreads between the streamline simulation models with the semi-analytical solution and the numerical solution. From the comparison of computing time, the streamline simulation using the semi-analytical solution is 10-200 times faster than the streamline simulation using the numerical solution. If we would use a semi-analytical solution instead of a numerical solution in case no analytical solution is available, we could obtain faster and more accurate simulation results free from numerical dispersion. [ABSTRACT FROM AUTHOR]

We study transport properties of bulk-disordered quasi-one-dimensional (Q1D) wires paying main attention to the role of long-range correlations embedded into the disorder. First, we show that for stratified disorder for which the disorder is the same for all individual chains forming the Q1D wire, the transport properties can be analytically described provided the disorder is weak. When the disorder in every chain is not the same, however it has the same binary correlator, the general theory is absent. Thus, we consider the case when only one channel is open and all others are closed. For this situation we suggest a semianalytical approach which is quite effective for the description of the total transmission coefficient. Our numerical data confirm the validity of this approach. [ABSTRACT FROM AUTHOR]