Numerical Implementation of BDF2 via Method of Lines for Time Dependent Nonlinear Burgers’ Equation

In this paper an efficient unconditionally stable numerical scheme is proposed for solving one dimensional quasi linear Burgers’ equation. The proposed scheme comprises of semi discretization via method of lines for the space variable and backward differentiation formula of order two (BDF2) for the time variable. The method of lines reduces the quasi linear partial differential equation in to nonlinear ordinary differential equations at each node point. The resulting nonlinear system is solved by an efficient stiff solver known as BDF2. BDF2 is an implicit solver which leads to nonlinear algebraic system and the resulting nonlinear algebraic system is linearized via Taylor series. This linearization technique is easy to implement and the accuracy of the method will remain unchanged. The linearized system of algebraic equations is solved using MATLAB 8.0. The proposed scheme is implemented on test examples and it has been observed that the numerical solution lies very close to the exact solution. Various numerical experiments have been carried out to demonstrate the performance of the method. Index Terms – Burgers’ equation ; Kinematic viscosity; Method of lines; Backward Differentiation Formula; Taylor series. ——————————  ——————————