Chebyshev wavelets for solving two-dimensional multi-noise stochastic integral equations in combination with block pulse functions

Abstract

In this investigation, our goal is to numerically solve two-dimensional Volterra-Fredholm stochastic integral equations with multiple  perturbations, using two-dimensional Chebyshev wavelets of the second kind as uni tary orthogonal bases. For this purpose, after  rewriting the functions in the stochastic integral equation based on two-dimensional Chebyshev wavelets of the second kind, to construct ordinary and random operational matrices, we expand these wavelets based on block pulse functions and, with the help of these expansions, obtain the desired operational matrices. These matrices result in a linear system, the solution of which will lead to the numerical solution of our stochastic integral equation. The estimation and analysis of the convergence of the proposed method, along with the examples provided, the average error at different points, the %95 confidence interval and the comparison of our method with other common methods, demonstrate the efficiency and accuracy of this method well.