Collocation solution of the Korteweg–de Vries equation using septic splines

Abstract

Numerical solutions for the Korteweg–de Vries equation based on the collocation method using septic splines as element shape functions are set up. A linear stability analysis of the scheme shows the method to be unconditionally stable. A test problem concerning the development and motion of solitons is used to validate the method. The numerical scheme is compared with other published methods and shown to be accurate and efficient.

Keywords:

• KdV equation
• Septic spline
• Collocation solution