Numerical simulation of the burger's equation

In this study, the exponential finite difference technique has been used to solve one-dimensional Burgers’ equation with different value of h (step size). Burgers’ equation is considered in this study because the equation governing simple nonlinear diffusion process. Since Burgers’ equation is nonlinear equation, the Hopf-Cole transformation has been applied to convert the equation to one-dimensional heat equation. Consequently, the exponential finite difference method has been used to generate of one-dimensional heat equation. Three techniques called explicit exponential finite difference method, implicit exponential finite difference method and modified Burgers’ equation using explicit exponential finite difference method have been implemented. In the solution process, the explicit exponential finite difference method used a direct to solve the Burgers’ equation while the implicit exponential finite difference method leads to a system of nonlinear equation. At each time-level, Newton’s method is used to solve the nonlinear system. The solution of the onedimensional modified Burgers’ equation by using the explicit exponential finite difference method. The solution process have been discretized the time derivative and spatial derivative using exponential finite difference technique. Numerical solutions for each method are compared with exact solution and the results obtained using three methods are precise and reliable. The percent errors are compute and found to be sufficiently small.