Numerical solution of seventh order KdV equations via quintic B-splines collocation method

Abstract

This paper proposes an approach based on the collocation technique with fifth-degree B-splines to numerically solve higher-order Korteweg–de-Vries (KdV) equations. The discretization of the temporal part is performed via a finite difference scheme and the quintic B-spline approximates the function and its derivatives. Consequently, the equation leads to an algebraic system being solved using matrices. The stability of the proposed scheme is also discussed and is found to be unconditionally stable. The solved test problems exhibit the accuracy and stability of the technique. The error is computed using the L∞ norm and the L2 norm. When compared to previous results, the observations suggest that the technique is better than many other methods present in the literature.

Keywords

• KdV equations
• Quintic B-spline
• Von Neumann stability