Solvability of partial differential equations by meshless kernel methods

Y. C. Hon; Robert Schaback

doi:10.1007/s10444-006-9023-2

Solvability of partial differential equations by meshless kernel methods

Y. C. Hon
, Robert Schaback

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

19 Citations (Scopus)

Abstract

This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then it is proven that any well-posed linear problem in strong or weak form can be solved by certain meshless kernel methods to any prescribed accuracy. © 2006 Springer Science+Business Media B.V.

Original language	English
Pages (from-to)	283-299
Journal	Advances in Computational Mathematics
Volume	28
Issue number	3
DOIs	https://doi.org/10.1007/s10444-006-9023-2
Publication status	Published - Apr 2008

Research Keywords

Kernel
Meshless
Partial differential equations
Solvability

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10.1007/s10444-006-9023-2

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title = "Solvability of partial differential equations by meshless kernel methods",

abstract = "This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then it is proven that any well-posed linear problem in strong or weak form can be solved by certain meshless kernel methods to any prescribed accuracy. {\textcopyright} 2006 Springer Science+Business Media B.V.",

keywords = "Kernel, Meshless, Partial differential equations, Solvability",

author = "Hon, \{Y. C.\} and Robert Schaback",

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TY - JOUR

T1 - Solvability of partial differential equations by meshless kernel methods

AU - Hon, Y. C.

AU - Schaback, Robert

PY - 2008/4

Y1 - 2008/4

N2 - This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then it is proven that any well-posed linear problem in strong or weak form can be solved by certain meshless kernel methods to any prescribed accuracy. © 2006 Springer Science+Business Media B.V.

AB - This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then it is proven that any well-posed linear problem in strong or weak form can be solved by certain meshless kernel methods to any prescribed accuracy. © 2006 Springer Science+Business Media B.V.

KW - Kernel

KW - Meshless

KW - Partial differential equations

KW - Solvability

UR - https://www.scopus.com/pages/publications/40849098576

UR - https://www.scopus.com/pages/publications/40849098576#tab=impact

U2 - 10.1007/s10444-006-9023-2

DO - 10.1007/s10444-006-9023-2

M3 - RGC 21 - Publication in refereed journal

SN - 1019-7168

VL - 28

SP - 283

EP - 299

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

IS - 3

ER -

Solvability of partial differential equations by meshless kernel methods

Abstract

Research Keywords

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Errata: The Publisher: Solvability of partial differential equations by meshless kernel methods (Advances in Computational Mathematics 28:3 (283-299) DOI 10.1007/s10444-006-9023-2)

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