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

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

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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
Volume29
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

Fingerprint

Ignition
System of Differential Equations
Coupled System
Numerical methods
Finite Difference
Differential equations
Continuous Solution
Numerical Methods
Numerical Solution
Monotone Iterative Method
Monotone Iteration
Monotone Scheme
Blow-up Time
Finite Time Blow-up
Blow-up Solution
Computational Algorithm
Automobile
First order differential equation
Iterative Scheme
Discrete Systems

Keywords

  • 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

Cite this

Numerical methods for a coupled system of differential equations arising from a thermal ignition problem. / Pao, C. V.; Chang, Yu-Hsien; Jau, Guo Chin.

In: Numerical Methods for Partial Differential Equations, Vol. 29, No. 1, 01.01.2013, p. 251-279.

Research output: Contribution to journalArticle

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