Interpolation by hybrid Radial Basis Functions for solving nonlinear Volterra-Fredholm-Hammerstein integral equations (original) (raw)
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2020
This article is an attempt to obtain the numerical solution of functional linear Voltrra two-dimensional integral equations using Radial Basis Function (RBF) interpolation which isbased on linear composition of terms. By using RBF in functional integral equation, rst alinear system C = G will be achieved; then the coecients vector is de ned, and nally thetarget function will be approximated. In the end, the validity of the method is shown by anumber of examples.
Journal of Computational and Applied Mathematics, 2011
In this paper, we introduce a numerical method for the solution of two-dimensional Fredholm integral equations. The method is based on interpolation by Gaussian radial basis function based on Legendre-Gauss-Lobatto nodes and weights. Numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the method.
Application of radial basis function to approximate functional integral equations
Journal of Interpolation and Approximation in Scientific Computing, 2016
In the present paper, Radial Basis Function (RBF) interpolation is applied to approximate the numerical solution of both Fredlholm and Volterra functional integral equations. RBF interpolation is based on linear combinations of terms which include a single univariate function. Applying RBF in functional integral equation, a linear system ΨC = G will be obtain in which by defining coefficient vector C, target function will be approximiated. Finally, validity of the method is illustrated by some examples.
2021
An approach to approximate solution of higher dimensional Volterra-Fredholm integral equations (VFIE) is presented in this paper. A well-established semi analytical method is extended to solution of VFIE for the first time, called Optimal Homotopy Asymptotic Method (OHAM). The efficiency and effectiveness of the proposed technique is tested upon (1+ 1) and (2+ 1) dimensional VFIE. Results obtained through OHAM are compared with multi quadric radial basis function method,radial basis function method, modified block-plus function method, Bernoulli collocation method, efficient pseudo spectral scheme, three dimensional block-plus function methods and 3D triangular function. The comparison clearly shows the effectiveness and reliability of the presented technique over these methods. Moreover, the use of OHAM is simple and straight forward.
A numerical method for solving Fredholm and Volterra integral equations is presented and analyzed. The method is essentially based on making use of Gauss quadrature formula. The second kind Chebyshev polynomials are used as basis functions. The main idea behind our algorithm depends on reducing the solution of the integral equation into a solution of algebraic system of equations which can be solved by a suitable numerical solver. Some illustrative examples are included to demonstrate the validity and applicability of the suggested algorithm.
Alternative Legendre polynomials (ALPs) are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given and the efficiency and accuracy are illustrated by applying the method to some examples.
Numerically Solving Volterra and Fredholm Integral Equations 1
2013
Abstract: Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) is known to be two powerful tools for solving many functional equations such as ordinary and partial differential and integral equations. In this paper (HAM) is applied to solve linear Fredholm and Volterra first and second kind integral equations, the deformation equations are solved analytically by using MATLAB integration functions. Numerical techniques for solving deformation equation are also applied using interpolation methods and Gaussian integration. Auxiliary parameter h is also used experimentally to control convergence of partial sum of series solution. Several examples are tested by these methods and numerical results are compared with exact solution or existing numerical results to demonstrate the efficiency of the methods. These methods can be generalized to non-linear Volterra and Fredholm integral equation. The analytical and numerical results show the performance and reliability of prese...
Numerically Solving Volterra and Fredholm Integral Equations
2012
Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) is known to be two powerful tools for solving many functional equations such as ordinary and partial differential and integral equations. In this paper (HAM) is applied to solve linear Fredholm and Volterra first and second kind integral equations, the deformation equations are solved analytically by using MATLAB integration functions. Numerical techniques for solving deformation equation are also applied using interpolation methods and Gaussian integration. Auxiliary parameter h is also used experimentally to control convergence of partial sum of series solution. Several examples are tested by these methods and numerical results are compared with exact solution or existing numerical results to demonstrate the efficiency of the methods. These methods can be generalized to non-linear Volterra and Fredholm integral equation. The analytical and numerical results show the perfo rmance and reliability of presented method.
An Appropriate Numerical Method for Solving Nonlinear Volterra-Fredholm Integral Equations
International Journal of Mathematics and Systems Science, 2018
This paper is concerned with the numerical solution of the mixed Volterra-Fredholm integral equations by using a version of the block by block method. This method efficient for linear and nonlinear equations and it avoids the need for spacial starting values. The convergence is proved and finally performance of the method is illustrated by means of some significative examples.