A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative. (23rd January 2021)

• Record Type: Journal Article
• Authors: Taghipour, M.; Aminikhah, H.
• Other Names: Zhang Li-Tao Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2021(2021)
• Publication Date: 2021-01-23
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2021/8837846
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of the coupled Burgers equations with the Caputo–Fabrizio derivative. The first- and second-order spatial derivatives have been approximated by first and second derivatives of the cubic B-spline quasi-interpolation. The discrete scheme obtained in this way constitutes a system of algebraic equations associated with a bi-pentadiagonal matrix. We show that the proposed scheme is unconditionally stable. Numerical examples are provided to verify the efficiency of the method.