A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers' equations

被引:1
|
作者
Dlamini, Phumlani G. [1 ]
Magagula, Vusi M. [2 ]
机构
[1] Univ Johannesburg, Dept Appl Phys & Engn Math, POB 17011, ZA-2028 Doornfontein, South Africa
[2] Univ Swaziland, Dept Math, Private Bag 4, Kwaluseni, Eswatini
关键词
Chebyshev spectral method; multivariate; quasi-linearization; COLLOCATION METHOD;
D O I
10.1515/ijnsns-2019-0055
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers' equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.
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页码:683 / 691
页数:9
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