Collocation Method for Solving the Generalized KdV Equation  

作　　者：Turabi Geyikli Turabi Geyikli(Department of Mathematics, Faculty of Education, Adiyaman University, Adiyaman, Turkey)

机构地区：[1]Department of Mathematics, Faculty of Education, Adiyaman University, Adiyaman, Turkey

出　　处：《Journal of Applied Mathematics and Physics》2020年第6期1123-1134,共12页应用数学与应用物理（英文）

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.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.

关 键 词：Generalized Korteweg-de Vries Equation Finite Element Method COLLOCATION Septic B-Spline SOLITON 

分 类 号：O17[理学—数学]