A Brief Description of Higher-Order Accurate Numerical Solution of Burgers’ Equation

Two new higher-order accurate finite-difference schemes for the numerical solution of boundary-value problem of the Burgers’ equation are suggested. Burgers equation is a one-dimensional analogue of the Navier-Stokes equations describing the dynamics of fluids and it possesses all of its mathematical properties. Besides the Burgers’ equation, one of the few nonlinear partial differential equations which has the exact solution, and it can be used as a test model to compare the properties of different numerical methods. A first scheme is purposed for the numerical solution of the heat equation. It has a sixth-order approximation in the space variable, and a third-order one in the time variable. A second scheme is used for finding a numerical solution for the Burgers’s equation using the relationship between the heat and Burgers’ equations. This scheme also has a sixth-order approximation in the space variable. The numerical results of test examples are found in good agreement with exact solutions and confirm the approximation orders of the schemes proposed.

Burgers’ equation, higher-order accurate numerical solution