A Trigonometric Quintic B-Spline Basis Collocation Method for the KdV-Kawahara Equation

This paper considers an effective numerical collocation method for numerical solution of the KdV-Kawahara equation. This numerical method relies on a finite element formulation and spline interpolation with a trigonometric quintic B-spline basis. First, the KdV-Kawahara equation is reduced to a coupled equation via an auxiliary variable of the form v = u(xxx). The collocation method is then applied to the coupled equation together with the forward difference and the Crank-Nicholson formula. This results in a systemof algebraic equations in terms of time variables with the trigonometric quintic B-spline basis. For determination of the error between the numerical and exact solutions, the error norms L-2 and L-infinity are calculated. The results are illustrated by two numerical examples with their graphical representation and comparison with other methods.