Solving burger’s equantion using explicit finite difference method and method of line

Abstract

Burgers’ equation is a quasilinear differential equation can be solve either analytically or numerically. The analytical solutions use the Hopf-Cole transformation and reduced to diffusion equation. The focus of this research was to solve Burgers’ equation numerically by using Finite Difference Method (FDM) and Method of Line (MOL) by using Fourth Order Runge-Kutta (RK4). The accuracy of MOL obtained solutions depends on the type of Ordinary Differential Equation (ODE) method used. The results obtained from both numerical method were compared between Hopf-Cole transformation analytical solutions. The simulations is coded by using MATLAB software. From the comparison, both methods shown to be good numerical approximation as the results obtained near to the exact solution. As the increase of spatial step size, the solutions obtained with be more accurate followed by individual methods’ restrictions. Different time and viscosity coefficient also tested to observe the changes of Burgers’ equation solutions.