Spectral collocation solution of a generalized Hirota–Satsuma coupled KdV equation

Abstract

In this paper the solution of a generalized Hirota–Satsuma Korteweg–de Vires (KdV) equation using a pseudospectral method is presented. To reduce roundoff error we use some preconditionings. Firstly, we discretize the equation in space to obtain a system of time-dependent ordinary differential equations. Secondly, we solve the obtained system of ordinary differential equations using the fourth-order Runge–Kutta method. The method works very well because the absolute errors are very small.

Keywords:

• Generalized Hirota–Satsuma coupled KdV equation
• Pseudospectral method
• Pre-conditioning

Acknowledgements

The authors are most indebted to the referee(s) for very constructive suggestions.