A Taylor–Galerkin finite element method for the KdV equation using cubic B-splines

In this paper, to obtain accurate solutions of the Korteweg–de Vries (KdV) equation, a Taylor–Galerkin method is proposed based on cubic B-splines over finite elements. To tackle this a forward time-stepping technique is accepted in time. To see the accuracy of the proposed method, L2 and L∞L∞ error norms are calculated in three test problems. The numerical results are found to be in good agreement with exact solutions and with the literature. The applied numerical method has also been shown to be unconditionally stable. In order to find out the physical behaviour of more intricate models, this procedure has been seen to have a great potentiality.