A Chebyshev spectral collocation method for solving Kdv-Burgers equation

Abstract EN

A mixed spectral/ Runge-Kutta method is used to obtain numerical solutions of Kortewege–de Vries–Burgers’ (KdVB) equation.

The suggested method based on Chebyshev spectral collocation is used with Runge-Kutta method of order four.

This technique is accomplished by starting with a Chebyshev approximation for the higher order derivatives in the x -direction and generating approximations to the lower derivatives through successive integrations of the highest-order derivative.

The proposed technique reduces the problem to a system of ordinary differential equations in the t -direction.

The Runge-Kutta method of order four is used to solve this system.

Excellent numerical results have been obtained compared with the exact solution