Bicubic B-Spline Functions to Solve Linear Two-Dimensional Weakly Singular Stochastic Integral Equation

The purpose of this paper is to present an appropriate numerical method for solving linear two-dimensional weakly singular stochastic integral equations. This method is based on bicubic B-spline interpolation, Gauss–Legendre quadrature formula, and two-dimensional Ito approximation. The proposed method is used to transform the solution of mentioned problem to the linear system of algebraic equations which can be solved by using an appropriate method. Convergence analysis of the approach has been investigated. In the end, two examples are given to show efficiency and accuracy of the method and their numerical results are reported.