Error analysis of the Chebyshev collocation method for linear second-order partial differential equations

被引：12

作者：

Yuksel, Gamze ^{[1
]}

Isik, Osman Rasit ^{[2
]}

Sezer, Mehmet ^{[3
]}

机构：

[1] Mugla Sitki Kocman Univ, Dept Math, Fac Sci, TR-48000 Mugla, Turkey

[2] Mugla Sitki Kocman Univ, Fac Educ, Elemantary Math Educ Program, TR-48000 Mugla, Turkey

[3] Celal Bayar Univ, Fac Sci & Letters, Dept Math, TR-45040 Manisa, Turkey

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2015年 / 92卷 / 10期

关键词：

partial differential equations; Chebyshev collocation method; Chebyshev polynomial solutions; error analysis of collocation methods; residual correction procedure; POLYNOMIAL SOLUTIONS;

D O I：

10.1080/00207160.2014.966099

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this study is to apply the Chebyshev collocation method to linear second-order partial differential equations (PDEs) under the most general conditions. The method is given with a priori error estimate which is obtained by polynomial interpolation. The residual correction procedure is modified to the problem so that the absolute error may be estimated. Finally, the effectiveness of the method is illustrated in several numerical experiments such as Laplace and Poisson equations. Numerical results are overlapped with the theoretical results.

引用

页码：2121 / 2138

页数：18

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