Numerical solution of two-dimensional weakly singular stochastic integral equations on non-rectangular domains via radial basis functions

Abstract

In this paper, a meshfree method based on radial basis functions (RBFs) is applied to solve two-dimensional weakly singular stochastic integral equations on non-rectangular domains. RBFs interpolation together quadrature rule is used to transform the solution of mentioned problem to the linear system of algebraic equations which can be solved by using direct method or iterative method. The most important advantage of this scheme is that it is independent of the geometry of the region and so it can be applied for solving different kinds of integral equations on irregular domains. Convergence analysis and error estimate of the proposed method have been investigated. In order to show accuracy and efficiency of the proposed approach, it is applied to solve two examples and maximum error and the root mean squared error (RMS-error) are reported. The obtained results reveal that the suggested method is very accurate and efficient.