Solution of two-dimensional Fredholm integral equation via RBF-triangular method

Abstract

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.

Fredholm Integral Equations with Degenerate Kernel Method in Two Dimensional

“…Many problem in applied science for example in engineering can be translated into twodimensional (2D-FIEs). Fallahzadeh in (Fallahzadeh, 2012) used the Gsussian radial basis function and triangular method to solve (2D-FIEs). Ziyaee and Tari (Ziyaee &Tari, 2015 andAbdelaziz, 2022) used the differential transform approach to solve the problem.…”

The Regularization-Homotopy Method for the Two-Dimensional Fredholm Integral Equations of the First Kind

“…Research on the two-dimensional case has been getting more attention recently [8][9][10][11][12][13][14][15]. The main goal in this work is to extend the regularization-homotopy method introduced in [7] for one dimensional Fredholm integral equations of the first kind to two-dimensional Fredholm integral equations of the first kind.…”