Numerical solutions of the modified KdV Equation with collocation method
Authors :
Seydi Battal Gazi Karakoc 1*
Author Address :
1 Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektas Veli University, Nevsehir, 50300, Turkey.
*Corresponding author.
Abstract :
In this article, numerical solutions of the modified Korteweg-de Vries (MKdV) equation have been obtained by a numerical technique attributed on collocation method using quintic B-spline finite elements. The suggested numerical scheme is controlled by applying three test problems involving single solitary wave, interaction of two and three solitary waves. To check the performance of the newly applied method, the error norms, $L_{2}$ and $% L_{infty }$, as well as the three lowest invariants, $I_{1}$, $I_{2}$ and $% I_{3}$, have been calculated. The acquired numerical results are compared with some of those available in the literature. Linear stability analysis of the algorithm is also examined.
Keywords :
Modified Korteweg-de Vries equation; finite element method; collocation; quintic B-spline; soliton.
DOI :
Article Info :
Received : July 21, 2018; Accepted : November 26, 2018.
