A quintic B-spline finite elements scheme for the KdVB equation

被引：60

作者：

Zaki, SI ^{[1
]}

机构：

[1] Suez Canal Univ, Coll Sci, Dept Math, Ismailia, Egypt

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2000年 / 188卷 / 1-3期

关键词：

Korteweg de-Vries Burgers' equation; finite element method; quintic B-splines; collocation;

D O I：

10.1016/S0045-7825(99)00142-5

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

An algorithm for solving the Korteweg de-vries Burgers' (KdVB) equation, based on the collocalion method with quintic B-spline finite elements is set up to simulate the solutions of the KdV, Burgers' and the KdVB equations. The migration of solitary waves and temporal evolution of a Maxwellian initial pulse are studied for the KdV equation. Burgers' equation is solved for different values of Reynolds number. The time evaluation of the solutions of the KdVB equation with different values for the diffusion and dispersion coefficients is studied. Invariants and error norms are studied wherever possible to determine the conservation properties of the algorithm. A linear stability analysis shows the scheme to be unconditionally stable. (C) 2000 Elsevier Science S.A. All rights reserved.

引用

页码：121 / 134

页数：14

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