A Novel Approach to Compute the Numerical Solution of Variable Coefficient Fractional Burgers' Equation with Delay

In this article, we come up with a novel numerical scheme based on Haar wavelet (HW) along with nonstandard ‎finite difference (NSFD) scheme to solve time-fractional Burgers’ equation with variable diffusion coefficient and ‎time delay. In the solution process, we discretize the fractional time derivative by NSFD ‎ formula and spatial ‎derivative by HWs series expansion. We use the quasilinearisation process to linearize the nonlinear term. Also, ‎the convergence of the scheme is discussed. The efficiency and correctness of the proposed scheme are assessed ‎by ‎L∞-error and L۲‎ ‎-error norms.‎

Keywords:

Fractional Burgers’ equation , Nonstandard finite difference , Haar wavelets , Variable coefficient , Time delay