Block Method Coupled with the Compact Difference Schemes for the Numerical Solution of Nonlinear Burgers’ Partial Differential Equations

Abstract

In this paper, a novel block method is proposed to solve the nonlinear time dependent Burgers’ equation. The Burgers’ PDE is semi discretized in spatial direction by using the standard fourth-order compact difference schemes to yield system of nonlinear ordinary differential equations (ODE) in time.The resulting system of first-order ODE from the Burgers’ equation is approximated by a new derived Block method. The new two-step hybrid methods are developed through the Interpolation and Collocation techniques. The derived methods are applied as a block method for the numerical solution of the nonlinear Burgers’ Partial Differential Equations (PDE) which is of physical relevance. The proposed block scheme has been proven to be zero-stable, consistent and convergent, also saving computational time while maintaining good accuracy. The efficiency of the derived method is demonstrated using three test problems.