Collocation Method for Solving the Generalized KdV Equation

• 作者: Turabi Geyikli
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: Generalized Korteweg-de Vries Equation Finite Element Method COLLOCATION Septic B-Spline SOLITON
• 年，卷（期）: 2020,（6）
• 页码范围: 1123-1134
• 页数: 12页
• 分类号: O17

摘要

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, <em>L</em>₂ and <em>L</em>_∞ and invariants <em>I</em>₁, <em>I</em>₂ and <em>I</em>₃ have been calculated. Our numerical results are compared with some of those available in the literature.