A Computational Method for Solving Two-Dimensional Linear Fredholm Integral Equations of the Second Kind

Abstract

In this paper an expansion method, based on Legendre or any orthogonal polynomials, is developed to find numerical solutions of two-dimensional linear Fredholm integral equations. We estimate the error of the method, and present some numerical examples to demonstrate the accuracy of the method.2000 Mathematics subject classification: 65R20.

A Triangle Algorithm of Padé-Type Approximant for Two-Dimensional Fredholm Integral Equations of the Second Kind

“…For domain , some works treat the square case [4][5][6][7][8][9][10] and some are based on discrete Galerkin method [5], Monte Carlo methods [6], or piecewise approximating polynomials [7], Nytröm methods based on cubature rules obtained as the tensor product of two-variate Gaussian 2 Mathematical Problems in Engineering rules [8,10], and meshless method with complex factors [11]. Rational approximation has extensive application in engineering, technology and calculation [12][13][14][15][16][17][18].…”

“…According to the relations (9) and (11), we can from [19] obtain the following error formula with the linear functional form:…”

Numerical solution of linear Fredholm integral equations via two-dimensional modification of hat functions

“…The methods heretofore available which can solve high dimensional equations are the radial basis functions (RBFs) method [11,12], the spline functions method [13], the block pulse functions (BPFs) method [14], the spectral methods such as collocation and Tau method [9,10,[15][16][17], Nystroms method [4,7], transform methods [18], Adomian decomposition method (ADM) [19][20][21], wavelets methods [22] and many other methods [23][24][25].…”

Numerical solution of nonlinear two-dimensional integral equations using rationalized Haar functions

“…In [14], Tari and Shahmorad have developed a method based on a basis of orthogonal polynomials for the numerical solution of linear two-dimensional VIE. sup 06t61 jf ðtÞ À S n ðtÞj 6 12x 1 n ; f ; n ¼ 1; 2; .…”