An effective application of differential quadrature method based onmodified cubic B-splines to numerical solutions of the KdV equation

Authors

ALİ BAŞHAN

DOI

10.3906/mat-1609-69

Abstract

In this study, numerical solutions of the third-order nonlinear Korteweg--de Vries (KdV) equation are obtained via differential quadrature method based on modified cubic B-splines. Five different problems are solved. To show the accuracy of the proposed method, $L_{2}$ and $L_{\infty }$ error norms of the problem, which has an analytical solution, and three lowest invariants are calculated and reported. The obtained solutions are compared with some earlier works. Stability analysis of the present method is also given.

Keywords

KdV equation, differential quadrature method, modified cubic B-splines, partial differential equation, stability

First Page

373

Last Page

394

Recommended Citation

BAŞHAN, ALİ (2018) "An effective application of differential quadrature method based onmodified cubic B-splines to numerical solutions of the KdV equation," Turkish Journal of Mathematics: Vol. 42: No. 1, Article 31. https://doi.org/10.3906/mat-1609-69
Available at: https://journals.tubitak.gov.tr/math/vol42/iss1/31