Stochastic operational matrix of Chebyshev wavelets for solving multi-dimensional stochastic Ito-Volterra integral equations

In this paper, the numerical solutions of multi-dimensional stochastic Ito-Volterra integral equations have been obtained by second kind Chebyshev wavelets. The second kind Chebyshev wavelets are orthonormal and have compact support on [0,1]. The block pulse functions and their relations to second kind Chebyshev wavelets are employed to derive a general procedure for forming stochastic operational matrix of second kind Chebyshev wavelets. The system of integral equations has been reduced to a system of nonlinear algebraic equations and solved for obtaining the numerical solutions. Convergence and error analysis of the proposed method are also discussed. Furthermore, some examples have been discussed to establish the accuracy and efficiency of the proposed scheme.