Direct solution of ill-posed boundary value problems by radial basis function collocation method

Numerical solution of ill‐posed boundary value problems normally requires iterative procedures. In a typical solution, the ill‐posed problem is first converted to a well‐posed one by assuming the missing boundary values. The new problem is solved by a conventional numerical technique and the solutio...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 64; no. 1; pp. 45 - 64
Main Authors: Cheng, A. H.-D., Cabral, J. J. S. P.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 07.09.2005
Wiley
Subjects:
Cauchy problem
collocation method
Computational techniques
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
ill-posed problem
inverse problem
Mathematical methods in physics
meshless method
Physics
radial basis function
Radial basis function
inverse problem
Inverse problems
Meshless method
Boundary-value problems
Modelling
Ill posed problem
Collocation method
Iterative methods
Optimization
ill-posed problem
Cauchy problem
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:Numerical solution of ill‐posed boundary value problems normally requires iterative procedures. In a typical solution, the ill‐posed problem is first converted to a well‐posed one by assuming the missing boundary values. The new problem is solved by a conventional numerical technique and the solution is checked against the unused data. The problem is solved iteratively using optimization schemes until convergence is achieved. The present paper offers a different procedure. Using the radial basis function collocation method, we demonstrate that the solution of certain ill‐posed problems can be accomplished without iteration. This method not only is efficient and accurate, but also circumvents the stability problem that can exist in the iterative method. Copyright © 2005 John Wiley & Sons, Ltd.
Bibliography:ArticleID:NME1362
Brazilian government
Federal University of Pernambuco
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SourceType-Scholarly Journals-1
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content type line 23
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.1362