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

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.