Title: Numerical treatment and analysis for a class of time-fractional Burgers equations with the Dirichlet boundary conditions

Authors: A.S.V. Ravi Kanth; Neetu Garg

Addresses: Department of Mathematics, National Institute of Technology, Kurukshetra, Haryana – 136119, India ' Department of Mathematics, National Institute of Technology, Kurukshetra, Haryana – 136119, India

Abstract: This paper aims to study a class of time-fractional Burgers equations with the Dirichlet boundary conditions in the Caputo sense. The Burgers equation occurs in the study of fluid dynamics, turbulent flows, acoustic waves, and heat conduction. We discretise the equation by employing the Crank-Nicolson finite difference quadrature formula in the direction of time. We then discretise the resulting equations in space domain using the exponential B-splines. A rigorous study of stability and convergence analysis is analysed. Several test problems are studied to illustrate the efficacy and feasibility of the proposed method. Numerical simulations confirm the coherence with the theoretical analysis. Comparisons with the other existing results in the literature indicate the effectiveness of the method.

Keywords: exponential B-spline; time-fractional Burgers equation; TFBE; Caputo fractional derivative.

DOI: 10.1504/IJCSE.2022.120789

International Journal of Computational Science and Engineering, 2022 Vol.25 No.1, pp.74 - 90

Received: 25 Oct 2020
Accepted: 22 Mar 2021
Published online: 08 Feb 2022 *

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