Numerical Solution of Burgers Equation using Cubic B-Spline Collocation Method and Neumann Boundary Condition

Abstract

Burgers equation is one of the nonlinear differential equations which is generally difficult to determine its analytical solution, so it is necessary to do a numerical approach. This article discusses the numerical solution of the Burgers equation using the Cubic B-Spline Collocation method. The first step is to derive the numerical scheme using the Cubic B-Spline Collocation method for the space variable and the Crank-Nicholson method for the time variable. Furthermore, based on von Neumann stability analysis, it is obtained that the numerical scheme of Burgers equation is unconditionally stable. By performing numerical simulations using different and step sizes, it can be shown that the absolute value of the resulting error will be smaller for the step sizes of and which is getting smaller.