Analysis of nonlinear Burgers equation with time fractional Atangana-Baleanu-Caputo derivative

Abstract

This paper demonstrates, a numerical method to solve the one and two dimensional Burgers' equation involving time fractional Atangana-Baleanu Caputo (ABC) derivative with a non-singular kernel. The numerical stratagem consists of a quadrature rule for time fractional (ABC) derivative along with Haar wavelet (HW) approximations of one and two dimensional problems. The key feature of the scheme is to reduce fractional problems to the set of linear equations via collocation procedure. Solving the system gives the approximate solution of the given problem. To verify the effectiveness of the developed method five numerical examples are considered. Besides this, the obtained simulations are compared with some published work and identified that proposed technique is better. Moreover, computationally the convergence rate in spatiotemporal directions is presented which shows order two convergence. The stability of the proposed scheme is also described via Lax-Richtmyer criterion. From simulations it is obvious that the scheme is quite useful for the time fractional problems.

Keywords

• Atangana-Baleanu-Caputo derivative
• Nonlinear problems
• Order of convergence
• Stability analysis