Numerical solution of multi-dimensional Itô Volterra integral equations by the second kind Chebyshev wavelets and parallel computing process

This paper presents a numerical method based on the least squares method and the second kind Chebyshev wavelets for solving the multi-dimensional Itô Volterra integral equations. The multi-dimensional Itô Volterra integral equation is converted to a non-square linear system of equations by Clenshaw-Curtis quadrature rules, then the least squares solution is obtained by the QR factorization method. As the multi-dimensional Itô Volterra integral equations are computationally intensive, we have used the parallel computing process to find the numerical solutions with reduced computation time. The convergence rate of the presented method is proven. Numerical results show the reliability and efficiency of the presented method.