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Irk, D., Dağ, I. and Saka, B. (2006) A Small Time Solutions for the Korteweg--de Vries Equation Using Spline Approximation. Applied Mathematics and Computation, 173, 834-846.
https://doi.org/10.1016/j.amc.2005.04.018

has been cited by the following article:

• 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.