TITLE:
Collocation Method for Solving the Generalized KdV Equation
AUTHORS:
Turabi Geyikli
KEYWORDS:
Generalized Korteweg-de Vries Equation, Finite Element Method, Collocation, Septic B-Spline, Soliton
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.6,
June
11,
2020
ABSTRACT: In this work, we have obtained numerical solutions of the generalized Korteweg-de Vries (GKdV) equation by using septic B-spline collocation finite element method. The suggested numerical algorithm is controlled by applying test problems including; single soliton wave. Our numerical algorithm, attributed to a Crank Nicolson approximation in time, is unconditionally stable. To control the performance of the newly applied method, the error norms, L2 and L∞ and invariants I1, I2 and I3 have been calculated. Our numerical results are compared with some of those available in the literature.