Efficient Solution of Burgers', Modified Burgers' and KdV-Burgers' Equations Using B-Spline Approximation Functions

被引：6
作者：
Parumasur, Nabendra [1 ]
Adetona, Rasheed A. [1 ]
Singh, Pravin [1 ]
机构：
[1] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, Private Bag X54001, ZA-4000 Durban, South Africa
来源：
MATHEMATICS | 2023年 / 11卷 / 08期
关键词：
B-spline; orthogonal collocation; finite element; Burgers' equation; NUMERICAL-SOLUTION; COLLOCATION METHOD; SCHEME;
D O I：
10.3390/math11081847
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper discusses the application of the orthogonal collocation on finite elements (OCFE) method using quadratic and cubic B-spline basis functions on partial differential equations. Collocation is performed at Gaussian points to obtain an optimal solution, hence the name orthogonal collocation. The method is used to solve various cases of Burgers' equations, including the modified Burgers' equation. The KdV-Burgers' equation is considered as a test case for the OCFE method using cubic splines. The results compare favourably with existing results. The stability and convergence of the method are also given consideration. The method is unconditionally stable and second-order accurate in time and space.
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页数：21
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