Numerical Treatment of the Modified Burgers’ Equation via Backward Differentiation Formulas of Orders Two and Three

Abstract

Abstract We present an efficient numerical method for solving the nonlinear modified Burgers’ equation (MBE) using the multi-step method. The nonlinear MBE is first discretized along the spatial direction alone by using the method of lines technique, and this method converts the MBE to a nonlinear system of ordinary differential equations. Multistep methods are employed to solve the nonlinear system of ordinary differential equations. Applicability of the proposed numerical techniques is established through test examples. Discrete root mean square error norm ( L 2 ) $(L_{2})$ and maximum error norm ( L ∞ ) $(L_{\infty})$ are computed and presented for demonstrating the accuracy of the present numerical method. Numerical experiments supported by figures shows that the proposed numerical scheme shows excellent agreement with exact solution and is superior to some existing numerical methods.