Numerical solutions of nonlinear two-dimensional partial Volterra integro-differential equations by Haar wavelet

Integral Equations, Origin, and Basic Tools Modeling of Problems as Integral Equations Volterra Integral Equations The Green's Function Fredholm Integral Equations Existence of the Solutions: Basic Fixed Point Theorems Higher Quadrature Rules for the Numerical Solutions Appendices Answers to Exercises References Index.

Introduction to integral equations with applications, by Abdul J. Jerri. Pp 254. $47·50. 1985. ISBN 0-8247-7293-8 (Marcel Dekker)

In this paper, a new reliable technique, which is based on hybrid functions approximation, is introduced for the approximate solutions of two-dimensional nonlinear Fredholm and Volterra integral equations. The properties of block-pulse functions together with the Taylor series are used to reduce the problem to the solution of nonlinear algebraic equations. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results show reliability and efficiency of the proposed method.

A computational method based on hybrid of block-pulse functions and Taylor series for solving two-dimensional nonlinear integral equations

In this paper, a new method is introduced to solve a two-dimensional Fredholm integral equation. The method is based on the approximation by Gaussian radial basis functions and triangular nodes and weights. Also, a new quadrature is introduced to approximate the two dimensional integrals which is called the triangular method. The results of the example illustrate the accuracy of the proposed method increases.

http://www.ispacs.com/journals/jiasc/2012/jiasc-00002/article.pdf

Solution of Two-dimensional Fredholm Integral Equation via RBF-triangular Method

A novel numerical method is developed for solving two-dimensional linear Fredholm integral equations of the second kind by integral mean value theorem. In the proposed algorithm, each element of the generated discrete matrix is not required to calculate integrals, and the approximate integral operator is convergent according to collectively compact theory. Convergence and error analyses of the approximate solution are provided. In addition, an algorithm is given. The reliability and efficiency of the proposed method will be illustrated by comparison with some numerical results.

/pdf/a-novel-numerical-method-of-two-dimensional-fredholm-3v14f9psjt.pdf

Sima Piroozfar

Papers

Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions

Numerical solution of linear Fredholm integral equations via modified Simpson’s quadrature rule