Jacobi Operational Matrix and its Application for Solving Systems of ODEs

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• 作者：A. Borhanifar ; M. M. Khader
• 关键词：Systems of ordinary differential equations ; Operational matrix ; Jacobi polynomials ; Spectral methods ; Convergence analysis
• 刊名：Differential Equations and Dynamical Systems
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：24
• 期：4
• 页码：459-473
• 全文大小：508 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  
• 出版者：Springer India
• ISSN：0974-6870
• 卷排序：24

文摘

In this paper, we implement the shifted Jacobi operational matrix of derivative with spectral tau method and collocation method for numerical solution for the systems of linear and non-linear ordinary differential equations subject to initial or boundary conditions. By means of this approach, such problems are reduced for solving a system of algebraic equations and are greatly simplified the problems. We compare the obtained numerical results with the exact solutions. Also, we present and prove several theorems, which are related to the convergence of the proposed methods. Finally, some numerical test examples are presented to illustrate the validity and the great potential of the proposed technique.