Search

This paper deals with the design and analysis of a robust numerical scheme based on an improvised quartic B-spline collocation (IQBSC) method for a class of nonlinear derivative dependent singular boundary value problems (DDSBVP). The convergence analysis of the method is studied by means of Green's function approach. It should be pointed out that the numerical order of convergence of standard quartic B-spline collocation (SQBC) scheme for second-order boundary value problems (BVPs) is four, however, our proposed IQBSC method is shown to be sixth order convergence. To illustrate the applicability and accuracy of the method, we consider eight test problems. The obtained results are compared to those from some existing numerical schemes in order to show the advantage of present method. It is shown that the rate of convergence of present numerical scheme is higher than that of some of existing numerical methods. The CPU time of the present numerical method is provided. [ABSTRACT FROM AUTHOR]

Adequate mathematical models and computational algorithms are developed in this study to investigate specific features of the deformation processes of elastic rotational shells at large displacements and arbitrary rotation angles of the normal line. A finite difference method (FDM) is used to discretize the original continuum problem in spatial variables, replacing the differential operators with a second-order finite difference approximation. The computational algorithm for solving the nonlinear boundary value problem is based on a quasi-dynamic form of the ascertainment method with the construction of an explicit two-layer time-difference scheme of second-order accuracy. The influence of physical and mechanical characteristics of isotropic and composite materials on the deformation features of elastic spherical shells under the action of surface loading of "tracking" type is investigated. The results of the studies conducted have shown that the physical and mechanical characteristics of isotropic and composite materials significantly affect the nature of the deformation of the clamped spherical shell in both the subcritical and post-critical domains. The developed mathematical models and computational algorithms can be applied in the future to study shells of rotation made of hyperelastic (non-linearly elastic) materials and soft shells. [ABSTRACT FROM AUTHOR]

We discuss numerical solution of boundary value problems for systems of nonlinear ordinary differential equations with a time singularity, x ′ (t) = M (t) t x (t) + f (t , x (t)) t , t ∈ (0 , 1 ] , b (x (0) , x (1)) = 0 , where M : [ 0 , 1 ] → R n × n and f : [ 0 , 1 ] × R n → R n are continuous matrix-valued and vector-valued functions, respectively. Moreover, b : R n × R n → R n is a continuous nonlinear mapping which is specified according to a spectrum of the matrix M (0) to guarantee the BVP to be well-posed. For the case where M (0) has eigenvalues with nonzero real parts, we prove new convergence results for the collocation method and analytical results about the necessary smoothness of the solution to the problem required in the numerical analysis. We illustrate the theory by means of numerical examples. [ABSTRACT FROM AUTHOR]

An analytical model is developed to study the Darcy flows in viscoelastic convection from an inclined plate as a simulation of electro-conductive polymer materials processing with Biot number effects. The Jeffery's viscoelastic model describes the non-Newtonian characteristics of the fluid and provides a good approximation for polymers, which constitutes a novelty of the present work. The normalized nonlinear boundary value problem is solved computationally with the Keller Box implicit finite difference technique. Extensive solutions for velocity, surface temperature, skin friction and heat transfer rate are visualized numerically and graphically for various thermophysical parameters. Validation is conducted with earlier published work for the case of a vertical plate in the absence of non-Newtonian effects. The boundary layer flow is accelerated with increase in Deborah number, whereas temperatures are decelerated slightly. Temperatures are boosted with increase in inclination parameter, whereas velocity is lowered. A reverse trend is seen for increasing mixed convection parameter. Increase in Biot number enhances both velocity and temperature. Increasing Darcy number is found to enhance velocity, whereas it suppresses temperature. This particle study finds applications in different industries like reliable equipment design, nuclear plants, gas turbines and different propulsion devices. [ABSTRACT FROM AUTHOR]

Copyright of System Research & Information Technologies / Sistemnì Doslìdžennâ ta Ìnformacìjnì Tehnologìï is the property of Institute for the Applied System Analysis at the NTUU KPI and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered. The ensuing problem involves proportional type delay terms and constitutes a subclass of delay differential equations known as pantograph. On using fixed point theorems due to Banach and Schaefer, some sufficient conditions are developed for the existence and uniqueness of the solution to the problem under investigation. Furthermore, due to the significance of stability analysis from a numerical and optimization point of view Ulam type stability and its various forms are studied. Here we mention different forms of stability: Hyers–Ulam (HU), generalized Hyers–Ulam (GHU), Hyers–Ulam Rassias (HUR) and generalized Hyers–Ulam–Rassias (GHUR). After the demonstration of our results, some pertinent examples are given. [ABSTRACT FROM AUTHOR]

The unavailability of wasted energy due to the irreversibility in the process is called the entropy generation. An irreversible process is a process in which the entropy of the system is increased. The second law of thermodynamics is used to define whether the given system is reversible or irreversible. Here, our focus is how to reduce the entropy of the system and maximize the capability of the system. There are many methods for maximizing the capacity of heat transport. The constant pressure gradient or motion of the wall can be used to increase the heat transfer rate and minimize the entropy. The objective of this study is to analyze the heat and mass transfer of an Eyring-Powell fluid in a porous channel. For this, we choose two different fluid models, namely, the plane and generalized Couette flows. The flow is generated in the channel due to a pressure gradient or with the moving of the upper lid. The present analysis shows the effects of the fluid parameters on the velocity, the temperature, the entropy generation, and the Bejan number. The nonlinear boundary value problem of the flow problem is solved with the help of the regular perturbation method. To validate the perturbation solution, a numerical solution is also obtained with the help of the built-in command NDSolve of MATHEMATICA 11.0. The velocity profile shows the shear thickening behavior via first-order Eyring-Powell parameters. It is also observed that the profile of the Bejan number has a decreasing trend against the Brinkman number. When ηi → 0 (i = 1, 2, 3), the Eyring-Powell fluid is transformed into a Newtonian fluid. [ABSTRACT FROM AUTHOR]

Reproducing kernel Hilbert space method is given for nonlinear boundary‐value problems in this paper. Applying this technique, we establish a new algorithm to approximate the solution of such nonlinear boundary‐value problems. This technique does not need any background mesh and can easily be applied. In this technique, the solution is given in the form of a series. Representation of the solutions is obtained in the reproducing kernel Hilbert space. Additionally, the convergence of the presented method is demonstrated. Numerical examples are presented to show the ability of the method. We compare the reproducing kernel Hilbert space method with B‐spline collocation method. As seen in the tables, the reproducing kernel Hilbert space method gives better results. [ABSTRACT FROM AUTHOR]

Exponential sextic spline function is used for the numerical solution of nonlinear fourth-order two-point boundary value problems. Spline relations are derived and direct methods of order two, four and six are obtained. Convergence analysis of the methods is discussed. The proposed method is tested on linear and nonlinear problems. Comparisons are made to confirm the reliability and accuracy of the proposed technique. [ABSTRACT FROM AUTHOR]

For impulsive boundary value problems whose solutions encounter discontinuities (jumps) at a priori not known positions depending on the solution itself, numerical methods have not been considered so far. We extend the well-known shooting approach to this case, combining Newton iteration with the numerical solution of impulsive initial value problems. We discuss conditions necessary for the procedure to be well-defined, and we present numerical results for several examples obtained with an experimental code realized in MATLAB. 1 [ABSTRACT FROM AUTHOR]

We study the local convergence to equilibria, as time goes to infinity, of trajectories of semilinear wave systems with friction damping on the boundary and subject to nonlinear potential energy. Estimates for the speed of convergence are obtained in terms of the behavior of the nonlinear feedback close to the origin. As an example of application, we show that the trajectories of a sine-Gordon system with nonlinear boundary damping, approach equilibria at least polynomially. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to investigate a computational scheme for solving a class of nonlinear boundary integral equations which occurs as a reformulation of boundary value problems of Laplace's equations with nonlinear Robin boundary conditions. The method approximates the solution by the Galerkin method based on the use of moving least squares (MLS) approach as a locally weighted least square polynomial fitting. The discrete Galerkin method for solving boundary integral equations results from the numerical integration of all integrals appeared in the method. The numerical scheme developed in the current paper utilizes the non-uniform Gauss–Legendre quadrature rule to estimate logarithm-like singular integrals. Since the proposed method is constructed on a set of scattered points, it does not require any background mesh and so we can call it as the meshless local discrete Galerkin (MLDG) method. The scheme is simple and effective to solve boundary integral equations and its algorithm can be easily implemented. We also obtain the error bound and the convergence rate of the presented method. Finally, numerical examples are included to show the validity and efficiency of the new technique and confirm the theoretical error estimates. [ABSTRACT FROM AUTHOR]

In the paper, an equilibrium problem for elastic bodies with a thin elastic Timoshenko inclusion and a thin semirigid inclusion is analyzed. The inclusions are assumed to be delaminated from elastic bodies, thus forming a crack between the inclusions and the elastic matrix. Nonlinear boundary conditions are imposed at the crack faces to prevent a mutual penetration between the crack faces. The inclusions have a joint point. A passage to a limit is investigated as a rigidity parameter of the elastic inclusion goes to infinity. The limit model is investigated. Junction boundary conditions are found at the joint point for the problem analyzed as well as for the limit problem. [ABSTRACT FROM AUTHOR]

We use Galerkin finite element method (GFEM) to solve second order linear and nonlinear boundary value problems (BVPs). First we develop FEM formulation for a class of linear and nonlinear BVPs. Then we present convergence analysis of the method. Later, we give the solution of some nonlinear BVPs with Diritchlet, Neumann and Robin boundary conditions. All results are compared with the exact solution and sometimes with the results of the existing method to verify the convergence, stability and consistency of this method. The results are depicted graphically as well as in the tabular form. [ABSTRACT FROM AUTHOR]

In this paper, we study a nonlinear third-order multipoint boundary value problem by the monotone iterative method. We then obtain the existence of monotone positive solutions and establish iterative schemes for approximating the solutions. In addition, we extend the considered problem to the Riemann-Liouville-type fractional analogue. Finally, we give a numerical example for demonstrating the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with a non-linear second order ordinary differential equation with symmetric non-linear boundary conditions, where both of the nonlinearities are of power type. It provides results concerning the existence and multiplicity of positive solutions, both symmetric and non-symmetric, for values of parameters not considered before. The main tool is the shooting method. [ABSTRACT FROM AUTHOR]

We consider a nonlinear boundary-value problem of heat conduction for an isotropic infinite heat-sensitive layered plate with heat-insulated faces containing a foreign through thermally active inclusion. By using the proposed transformation, we perform partial linearization of the initial heat-conduction equation. As a result of a piecewise-linear approximation of temperatures on the boundary surfaces of the foreign layers and the inclusion, the equation is completely linearized. We find an analytic-numerical solution of this equation with boundary conditions of the second kind in order to determine the introduced function with the use of the Fourier integral transformation. The computational formulas for the unknown values of temperature are presented in the case of a linear temperature dependence of the heat-conduction coefficients of structural materials for the two-layer plates. The numerical analysis is performed for a single-layer plate containing a through thermally active inclusion (the material of the plate is VK94-I ceramic and the material of the inclusion is silver). [ABSTRACT FROM AUTHOR]

Forced vibration is investigated for two elastically connected cantilevers, under harmonic base excitation. One of the cantilevers is with a tip magnet repelled by a magnet fixed on the base. The cantilevers are uniform viscoelastic beams constituted by the Kelvin model. The system is formulated as a set of two linear partial differential equations with nonlinear boundary conditions. The method of multiple scales is developed to analyze the effects of internal resonances on the steady-state responses to external excitations in the nonlinear boundary problem of the partial differential equations. In the presence of 2:1 internal resonance, both the first and the second primary resonances are examined in detail. The analytical frequency–amplitude response relationships are derived from the solvability conditions. It is found that the frequency–amplitude response curves reveal typical nonlinear phenomena such as jumping and hysteresis in both primary resonances as well as saturation in the second primary resonance. The frequency–amplitude response curves may be converted from hardening-type single-jumping to double-jumpings, and further to softening-type single-jumping by adjusting the distance between two magnets. It is also found that the unstable parts of the frequency–amplitude response curves correspond to quasi-periodic motions. The finite difference scheme is proposed to discretize both the temporal and the spatial variables, and thus the numerical solutions can be calculated. The analytical results are supported by the numerical solutions. [ABSTRACT FROM AUTHOR]

In this paper, a novel numerical method is proposed for solving nonlinear boundary value problems. This method is based on a combination of the reproducing kernel and least squares methods. So the accuracy of this method is improved. We have proved the uniform convergence of the approximate solution u n by convergence of u n in W 3 [ a , b ] . Numerical results obtained by using the scheme show that the numerical scheme is feasible and effective. [ABSTRACT FROM AUTHOR]

A Rankine source method with a continuous desingularized free surface source panel distribution is developed to solve numerically a wave-body interaction problem with nonlinear boundary conditions. A body undergoes forced oscillatory motion in a free water surface and the variation of wetted body surface is captured by a regridding process. Free surface sources are placed in continuous panels, rather than points in isolation, over the calm water surface, with free surface collocation points placed on the calm water surface. Nonlinear kinematic and dynamic free surface boundary conditions along the collocation points on the calm water surface are solved in a time domain simulation based on a Lagrange time dependent formulation. Compared with isolated desingularized source points distribution methods, a significantly reduced number of free surface collocation points with sparse distribution are utilized in the present numerical computation. The numerical scheme of study is shown to be computationally efficient and the accuracy of numerical solutions is compared with traditional numerical methods as well as measurements. [ [ABSTRACT FROM AUTHOR]

This paper deals with the blow-up phenomena for a system of parabolic equations with nonlinear boundary conditions. We show that under some conditions on the nonlinearities, blow-up occurs at some finite time. We also obtain upper and lower bounds for the blow-up time when blow-up occurs. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We consider the second-order nonlinear boundary value problems (BVPs) with Sturm–Liouville boundary conditions. We define types of solutions and show that if there exist solutions of different types then there exist intermediate solutions also. [ABSTRACT FROM PUBLISHER]

In this paper, we study the blow-up singularity of a semilinear parabolic equation with nonlinear memory both in the reaction term and the boundary condition. We firstly establish the local solvability for a large class of semilinear parabolic equations with various nonlocal reaction terms. Secondly, we give a complete classification for the existence of a blow-up solution and a global solution. Next, we show that under some hypotheses the blow-up can only occur on the boundary of the domain. [ABSTRACT FROM AUTHOR]

Abstract: The classical numerical treatment of boundary value problems defined on infinite intervals is to replace the boundary conditions at infinity by suitable boundary conditions at a finite point, the so-called truncated boundary. A truncated boundary allowing for a satisfactory accuracy of the numerical solution has to be determined by trial and errors and this seems to be the weakest point of the classical approach. On the other hand, the free boundary approach overcomes the need for a priori definition of the truncated boundary. In fact, in a free boundary formulation the unknown free boundary can be identified with a truncated boundary and being unknown it has to be found as part of the solution. In this paper we consider a different way to overcome the introduction of a truncated boundary, namely non-standard finite difference schemes defined on quasi-uniform grids. A quasi-uniform grid allows us to describe the infinite domain by a finite number of intervals. The last node of such grid is placed on infinity so that right boundary conditions are taken into account exactly. We apply the proposed approach to the Falkner–Skan model and to a problem of interest in foundation engineering. The obtained numerical results are found in good agreement with those available in literature. Moreover, we provide a simple way to improve the accuracy of the numerical results using Richardson’s extrapolation. Finally, we indicate a possible way to extend the proposed approach to boundary value problems defined on the whole real line. [Copyright &y& Elsevier]

Basing ourselves on the subsolution and supersolution method we investigate the existence and properties of solutions of the following class of elliptic differential equations div(a(∥x∥)∇u(x)) + f(x; u(x)) + g(∥x∥)k(x ∙ ∇u(x)) = 0; x ∈ ℝn, ∥x∥ > R. Our main result concernes the behavior of solution at infinity. [ABSTRACT FROM AUTHOR]

This work is concerned with the numerical approximation of the unsteady Stokes flow of a viscous incompressible fluid driven by a threshold slip boundary condition of friction type. The continuous problem is formulated as variational inequality, which is next discretize in time based on backward Euler's scheme. We prove existence and uniqueness of the solution of the time discrete problem by means of a regularization approach. Finally, we derive error estimates that justify the convergence property of the discretization proposed. [ABSTRACT FROM AUTHOR]

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of power-law nonlinearity. In order to numerically solve this type of nonlinear boundary value problems, we construct a kind of spectral collocation method. The spatial approximation is based on shifted Jacobi polynomials Jn(α,β) (r) with α, β ∈ (-1,∞), r ∈ (0,1) and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes for the spectral method. After deriving the method for a rather general class of equations, we apply it to several specific examples. One natural example is a nonlinear boundary value problem related to the Yamabe problem which arises in mathematical physics and geometry. A number of specific numerical experiments demonstrate the accuracy and the efficiency of the spectral method. We discuss the extension of the method to account for more complicated forms of nonlinearity. [ABSTRACT FROM AUTHOR]

Two-point nonlinear boundary value problems (BVPs) in both unbounded and bounded domains are solved in this paper using fast numerical antiderivatives and derivatives of functions of L2(-∞, ∞). This differintegral scheme uses a new algorithm to compute the Fourier transform. As examples we solve a fourth-order two-point boundary value problem (BVP) and compute the shape of the soliton solutions of a one-dimensional generalized Korteweg-de Vries (KdV) equation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new technique for solving a class of nonlinear Boundary Value Problems (BVPs) is introduced. Convergence of the series solution obtained from the proposed technique is proved. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. Some numerical examples are introduced to verify the efficiency of the new technique. [Copyright &y& Elsevier]

An analytical solution of the spatial conjugate problem of heat transfer with constant thermophysical coefficients has been obtained. Conditions for the single-valued solvability of the nonlinear boundary-value problem have been found, and the rate of convergence of iteration process has been estimated. The results of test checkings of the analytical solution from Part 1 of the present article are given, and the assessment of the accuracy of formulas when compared with the well-known numerical method and analytical solution is presented. [ABSTRACT FROM AUTHOR]

Abstract: A three dimensional numerical analysis for unconfined seepage problems in inhomogeneous and anisotropic domains with arbitrary geometry is presented in this paper. The unconfined seepage problems are nonlinear in its nature due to unknown location of the phreatic surface and nonlinear boundary conditions which complicates its solution. The presented method is based on the application of non-boundary-fitted meshes and is an extension of the recently proposed two dimensional smoothed fixed grid finite element method. The main objective of using this method is to facilitate solution of variable domain problems and improve the accuracy of the formulation of the boundary intersecting elements. In this method, the gradient smoothing technique is used to obtain the element matrices. This technique simplifies the solution significantly by reducing the volume integrals over the elements into area integrals on the faces of smoothing cells. To locate the free surface, an initial guess for the unknown geometry is selected and modified in each iteration to eventually satisfy nonlinear boundary condition. The application of the proposed technique for three dimensional seepage problems is carried out for different examples including rectangular, trapezoidal and semi-cylindrical dams and the results are compared with those available in the literature. [Copyright &y& Elsevier]

In this paper, we propose an iterative method for solving a beam problem which is described by a nonlinear fourth-order equation with nonlinear boundary conditions. The method reduces this nonlinear fourth-order problem to a sequence of linear second-order problems with linear boundary conditions. The convergence of the method is proved, and some numerical examples demonstrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses flow control of fluids through porous media, specifically related to its application in petroleum science. The flow of fluids is described by the Boussinesq equation with mixed boundary conditions; a Neumann boundary condition describes no flow at the outer boundary of the porous media and a nonlinear boundary condition describes the interaction between the porous media and the source potential. In many ways, the source potential can be controlled. This leads to a boundary control problem of the Boussinesq equation. The problem can be analyzed by the Lyapunov method. Numerical examples are performed to provide a clear understanding of the concept of boundary control for these fluid flow systems. [Copyright &y& Elsevier]

Abstract: The present paper presents the finite element solution of two-dimensional non-linear singularly perturbed elliptic partial differential equation subject to appropriate Dirichlet boundary conditions. A new fifth order convergent Newton type iterative method has been described and used to linearize the non-linear problem. The inclusion of this Newton’s method of fifth order convergence in finite element method for solving non-linear system of equations reduces the number of iterations and hence the cost of computation. To demonstrate the usefulness of the proposed scheme, a non-convex variational Ginzburg–Landau equation is considered. [Copyright &y& Elsevier]

Abstract: In this paper, the temperature and velocity fields associated with the Falkner–Skan boundary-layer problem have been studied. The nonlinear boundary-layer equations are solved analytically by homotopy Perturbation method (HPM) employing Pade’ technique. Analytical results for the temperature and velocity of the flow are presented through graphs and tables for various values of the wedge angle and Prandtl number. It is seen that the current results in comparison with the numerical ones are in excellent agreement and the HPM–Pade’ solution provides a convenient way to control and adjust the convergence region of a system of nonlinear boundary-layer problems. [Copyright &y& Elsevier]

In this note, we first give two counterexamples to the comparison principles given by L. Chen and J. Sun [ J. Math. Anal. Appl. 325 (2007) 830-842]. Then we suggest and show corrected versions of the comparison principles. [ABSTRACT FROM AUTHOR]

In this paper, some methodology in nonlinear dynamics is used to study a boundary-value problem of a nonlinear model arisen in phase transitions in a slender cylinder composed of a compressible hyperelastic material. We transform the original system of boundary-value problem to an initial-value (dynamical) problem of finding periodic solutions of coupled nonlinear autonomous oscillators in a four-dimensional space. Hopf-like bifurcation analysis of the periodic solutions of the system is studied. Both analytical and numerical solutions are obtained by using a nonlinear transformation formulation. The accuracy of analytical solutions is investigated by comparing with the numerical solutions. The engineering stress-strain curve is plotted and compared with that from the normal form equation, which is a simplification of the original system. [ABSTRACT FROM AUTHOR]

We consider a boundary value problem with nonlinear boundary conditions. By using a suitable parametrization, we reduce the original problem to the parametrized one containing linear boundary restrictions. We construct a numerical-analytic scheme that is suitable for the study of the solutions of the transformed boundary value problem. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the pull-in instability of electrostatically actuated nanotweezers considering the dispersion forces is studied using distributed and lumped parameter models. By analogy to nanoswitches, closed-form solutions are obtained for electrostatic nanotweezers. The distributed and lumped parameter modeling of the tweezer result, respectively, in two coupled nonlinear boundary value problems and two coupled nonlinear equations, which are solved numerically in the cases of electrostatic microtweezers, freestanding nanotweezers, and electrostatic nanotweezers. In each case, analytical and numerical solutions are obtained and compared with those of the corresponding switch. In addition, the results of the distributed and lumped parameter models are compared. The detachment length and minimum initial gap of nanotweezers are determined. [Copyright &y& Elsevier]

Abstract: A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed. Numerical examples are illustrated. Numerical results show that the method is very effective. [Copyright &y& Elsevier]

In this research, we study about fractional order for nonlinear of fifth-order boundary value problems and produce a theorem for higher order of fractional of nth-order boundary value problems. The aim of this study was to evaluate and validate the theorem and provide several numerical examples to test the performance of our theorem. We also make comparison between exact solutions and differential transformation method(DTM) by calculating the error between them. It is shown that DTM has very small error and suitable in several numerical solutions since it is effective and provide high accuracy. [ABSTRACT FROM AUTHOR]

Abstract: A numerical method based on B-spline is developed to solve the general nonlinear two-point boundary value problems up to order 6. The standard formulation of sextic spline for the solution of boundary value problems leads to non-optimal approximations. In order to derive higher orders of accuracy, high order perturbations of the problem are generated and applied to construct the numerical algorithm. The error analysis and convergence properties of the method are studied via Green’s function approach. global error estimates are obtained for numerical solution of these classes of problems. Numerical results are given to illustrate the efficiency of the proposed method. Results of numerical experiments verify the theoretical behavior of the orders of convergence. [ABSTRACT FROM AUTHOR]

Fluid loads on a variety of hydraulic structures and the free surface profile of the flow are important for design purposes. This is a difficult task because the governing equations have nonlinear boundary conditions. The main objective of this paper is to develop a procedure based on the natural element method (NEM) for computation of free surface profiles, velocity and pressure distributions, and flow rates for a two-dimensional gravity fluid flow under sluice gates. Natural element method is a numerical technique in the field of computational mechanics and can be considered as a meshless method. In this analysis, the fluid was assumed to be inviscid and incompressible. The results obtained in the paper were confirmed via a hydraulic model test. Calculation results indicate a good agreement with previous flow solutions for the water surface profiles and pressure distributions throughout the flow domain and on the gate. [ABSTRACT FROM AUTHOR]