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.
Assabaai, Mubarak Awadh
"A Chebyshev Spectral Collocation Method for Solving Kdv-Burgers Equation,"
Hadhramout University Journal of Natural & Applied Sciences: Vol. 14
, Article 8.
Available at: https://digitalcommons.aaru.edu.jo/huj_nas/vol14/iss2/8