Numerical methods for a coupled system of differential equations arising from a thermal ignition problem

C. V. Pao, Yu-Hsien Chang, Guo Chin Jau

研究成果: 雜誌貢獻文章同行評審

6 引文 斯高帕斯(Scopus)

摘要

This article is concerned with monotone iterative methods for numerical solutions of a coupled system of a first-order partial differential equation and an ordinary differential equation which arises from fast-igniting catalytic converters in automobile engineering. The monotone iterative scheme yields a straightforward marching process for the corresponding discrete system by the finite-difference method, and it gives not only a computational algorithm for numerical solutions of the problem but also the existence and uniqueness of a finite-difference solution. Particular attention is given to the "finite-time" blow-up property of the solution. In terms of minimal sequence of the monotone iterations, some necessary and sufficient conditions for the blow-up solution are obtained. Also given is the convergence of the finite-difference solution to the continuous solution as the mesh size tends to zero. Numerical results of the problem, including a case where the continuous solution is explicitly known, are presented and are compared with the known solution. Special attention is devoted to the computation of the blow-up time and the critical value of a physical parameter which determines the global existence and the blow-up property of the solution. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013

原文英語
頁(從 - 到)251-279
頁數29
期刊Numerical Methods for Partial Differential Equations
29
發行號1
DOIs
出版狀態已發佈 - 2013 一月 1

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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