Using radial basis functions to solve two dimensional linear stochastic integral equations on non-rectangular domains

Abstract

The main goal of this paper is presenting an efficient numerical scheme to solve two dimensional linear stochastic integral equations on non-rectangular domains. The proposed method is based on combination of radial basis functions (RBFs) interpolation and Gauss–Legendre quadrature rule for double integrals. The most important advantage of proposed method is that it does not require any discretization and so it is independent of the geometry of the domains. Thus, many problems on the irregular domains can be solved. By using this method, the solution of consideration problem is converted to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. Also, the convergence analysis of this approach is discussed. Finally, applicability of the present method is investigated through illustrative examples.