A monotonicity procedure for the accurate, efficient solution of certain heat-transfer problems with variable thermal properties
type: Item
instance of: scholarly article
title: A monotonicity procedure for the accurate, efficient solution of certain heat-transfer problems with variable thermal properties
zbMATH Open document ID: 0829.65105
DOI: 10.1016/0377-0427(93)E0255-K
published in: Journal of Computational and Applied Mathematics
publication date: 1996-01-25T00:00:00Z
review text: The work is dedicated to the numerical solution of the nonlinear boundary value problem \[ a(F) F'' + b(F) (F')^2 = f(F),\;F = F(x), \;0 < x < 1;\;F'(0) = 0,\;F(1) = K = \text{const} > 0. \] Particular cases of this problem are discussed and studied. For them the Newton/Picard iterative schemes are presented; their convergence is proved. The peculiarities of the solutions of the discussed problems are stated. The discretization of the iterative schemes is carried out and the question of their stability is discussed. Results of numerical experiments of solving model examples with various initial data are presented. They are compared with the initial solutions obtained by other authors.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 777856
zbMATH Keywords: heat-transfer problems
zbMATH Keywords: nonlinear boundary value problem
zbMATH Keywords: Newton/Picard iterative schemes
zbMATH Keywords: convergence
zbMATH Keywords: stability
zbMATH Keywords: numerical experiments
author: J. W. Mooney
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 777856