- Turkish Journal of Mathematics
- Vol: 42 Issue: 1
- An effective application of differential quadrature method based on modified cubic B-splines to nume...
An effective application of differential quadrature method based on modified cubic B-splines to numerical solutions of the KdV equation
Authors : Ali Başhan
Pages : 373-394
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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