Particular solutions of Laplace and bi-harmonic operators using Matérn radial basis functions

In this paper, we derive closed-form particular solutions of Matérn radial basis functions for the Laplace and biharmonic operator in 2D and Laplace operator in 3D. These derived particular solutions are essential for the implementation of the method of particular solutions for solving various types...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 94; no. 4; pp. 690 - 706
Main Authors Lamichhane, A. R., Chen, C. S.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.04.2017
Taylor & Francis Ltd
Subjects
Computer simulation
Exact solutions
Laplace transforms
Mathematical analysis
Mathematical models
Matérn function
Operators (mathematics)
Partial differential equations
Radial basis function
Radial basis functions
the method of particular solutions
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Summary:In this paper, we derive closed-form particular solutions of Matérn radial basis functions for the Laplace and biharmonic operator in 2D and Laplace operator in 3D. These derived particular solutions are essential for the implementation of the method of particular solutions for solving various types of partial differential equations. Four numerical examples in 2D and 3D are given to demonstrate the effectiveness of the derived particular solutions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2015.1127359