Operational matrix of two dimensional Chebyshev wavelets and its applications in solving nonlinear partial integro-differential equations

Abstract

Purpose

This paper aims to present a new method for the approximate solution of two-dimensional nonlinear Volterra–Fredholm partial integro-differential equations with boundary conditions using two-dimensional Chebyshev wavelets.

Design/methodology/approach

For this purpose, an operational matrix of product and integration of the cross-product and differentiation are introduced that essentially of Chebyshev wavelets. The use of these operational matrices simplifies considerably the structure of the computation used for a set of the algebraic system has been obtained by using the collocation points and solved.

Findings

Theorem for convergence analysis and some illustrative examples of using the presented method to show the validity, efficiency, high accuracy and applicability of the proposed technique. Some figures are plotted to demonstrate the error analysis of the proposed scheme.

Originality/value

This paper uses operational matrices of two-dimensional Chebyshev wavelets and helps to obtain high accuracy of the method.

Citation

Rostami, Y. (2021), "Operational matrix of two dimensional Chebyshev wavelets and its applications in solving nonlinear partial integro-differential equations", Engineering Computations, Vol. 38 No. 2, pp. 745-761. https://doi.org/10.1108/EC-03-2020-0162