Chebyshev reproducing kernel method: application to two-point boundary value problems
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- 作者：M Khaleghi ; E Babolian ; S Abbasbandy
- 关键词：two ; point boundary value problem ; Dirichlet boundary conditions ; polynomial reproducing kernel ; Chebyshev polynomials ; convergence ; error estimation
- 刊名：Advances in Difference Equations
- 出版年：2017
- 出版时间：December 2017
- 年：2017
- 卷：2017
- 期：1
- 全文大小：1833KB
- 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
- 出版者：Springer International Publishing
- ISSN：1687-1847
- 卷排序：2017
文摘
In this paper, a new implementation of the reproducing kernel method is proposed in order to obtain the accurate numerical solution of two-point boundary value problems with Dirichlet boundary conditions. Based on reproducing kernel theory, reproducing kernel functions with polynomial form will be constructed in the reproducing kernel spaces spanned by the Chebyshev basis polynomials. Convergence analysis and an error estimation for the present method in \(L_{w}^{2}\) space is also discussed. The numerical solutions obtained by this method are compared with the exact solutions. The results reveal that the proposed method is quite efficient and accurate.