A Second-order Scheme for the Generalized Time-fractional Burgers' Equation

Abstract

Abstract A second-order numerical scheme is proposed to solve the generalized time-fractional Burgers' equation. Time-fractional derivative is considered in the Caputo sense. First, the quasilinearization process is used to linearize the time-fractional Burgers'; equation, which gives a sequence of linear partial differential equations (PDEs). The Crank-Nicolson scheme is used to discretize the sequence of PDEs in the temporal direction, followed by the central difference formulae for both the first and second-order spatial derivatives. The established error bounds (in the $L^2-$norm) obtained through the meticulous theoretical analysis show that the method is the second-order convergent in both space and time. The technique is also shown to be conditionally stable. Some numerical experiments are presented to confirm the theoretical results.