A Numerical Solution of Burger’s Equation Based on Milne Method

Abstract

Burger’s equation is a nonlinear parabolic partial differential equation used in several fields such as fluid dynamics and traffic flow. In this research, we find the numerical solution of the one-dimensional Burger’s equation by using the multi-step Milne method and the central finite difference approach. A linearization scheme with a weighted technique is employed to handle the nonlinear term. Due to the multistep approach, the second-order Runge-Kutta and Modified- Newton Raphson schemes are applied to determine the second initial condition. The numerical results are compared with the exact solution, where the L2and L∞norms of the errors are used to verify the accuracy of the techniques. The numerical solutions are in good agreement with the exact solution. Among various different variables in the governing equation and the initial condition, the numerical visualizations are provided for the different values of the parameters.