Operational matrix of two dimensional Chebyshev wavelets and its applications in solving nonlinear partial integro-differential equations. Issue 2 (3rd August 2020)

• Record Type: Journal Article
• Authors: Rostami, Yaser
• Is Part Of: Engineering computations. Volume 38:Issue 2(2021)
• Page Start: 745
• Page End: 761
• Publication Date: 2020-08-03
• Subjects: Operational matrices -- Chebyshev wavelets -- Integration product -- Partial integro-differential equations; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-03-2020-0162
• Languages: English
• ISSNs: 0264-4401

Abstract

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.