A computational procedure for solving a chemical flow reactor problem using shooting method
type: Item
instance of: scholarly article
title: A computational procedure for solving a chemical flow reactor problem using shooting method
zbMATH Open document ID: 0828.65101
DOI: 10.1016/0096-3003(94)00082-F
author: K. Selvakumar
published in: Applied Mathematics and Computation
publication date: 1996-01-10T00:00:00Z
review text: The paper deals with the chemical flow reactor problem \(\varepsilon u'' + a(t) u' - b(t)u = f(t)\), \(0 < t < 1\), \(B_0 u(0) \equiv - u'(0) = \phi_1\), \(B_1 u(1) \equiv u(1) + \varepsilon u' (1) = \phi_2\), where \(\varepsilon > 0\) is a small parameter and \(a\), \(b\) and \(f\) are smooth functions satisfying \(a(t) \geq \alpha > 0\) and \(b(t) \geq 0\) with respect to \(t\). The problem is solved using the shooting method, i.e. the given problem is transformed into an initial value problem and then the resultant problem is solved numerically using a known exponentially fitted finite difference scheme. The similarity between the given chemical reactor flow problem and the initial value problem is that the nonuniformity occurs only in the derivative but not in the solution. The advantage of this method is that there is no need for matrix inversions as in tridiagonal difference schemes. The convergence of the method is correctly proved and some numerical results are given to illustrate the computational procedure.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 80A32
zbMATH DE Number: 753908
zbMATH Keywords: chemical flow reactor problem
zbMATH Keywords: shooting method
zbMATH Keywords: exponentially fitted finite difference scheme
zbMATH Keywords: convergence
zbMATH Keywords: numerical results
reviewed by: Dana Petcu
MaRDI profile type: Publication
cites work: On singular perturbation of nonlinear two-point boundary value problems
cites work: Q3909948
cites work: A computational method for solving singular perturbation problems using exponentially fitted finite difference schemes
cites work: Q5674335
full work available at URL: 0096-3003(94)00082-f
OpenAlex ID: W2033742273
Wikidata QID: Q126982482
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description: scientific article; zbMATH DE number 753908