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

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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

Original languageEnglish
Pages (from-to)251-279
Number of pages29
JournalNumerical Methods for Partial Differential Equations
Issue number1
Publication statusPublished - 2013 Jan


  • blow-up solution
  • catalytic converter
  • finite difference solution
  • monotone iteration
  • system of first-order equations

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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