Volume 5, Issue 1
Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs

Ahmad Shirzadi & Leevan Ling

Adv. Appl. Math. Mech., 5 (2013), pp. 78-89.

Published online: 2013-05

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  • Abstract

This paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial basis function (RBF) kernels generated trial spaces. Local weak-form testings are done with step-functions. It is proved that subject to sufficiently many appropriate testings, solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed. Moreover, an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation. Numerical results (in double precision) give good agreement with the provided theory.

  • Keywords

Local integral equations, meshless methods, radial basis functions, overdetermined systems, solvability, convergence.

  • AMS Subject Headings

35J25, 65N12, 65D30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-78, author = {Shirzadi , Ahmad and Ling , Leevan}, title = {Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {1}, pages = {78--89}, abstract = {

This paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial basis function (RBF) kernels generated trial spaces. Local weak-form testings are done with step-functions. It is proved that subject to sufficiently many appropriate testings, solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed. Moreover, an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation. Numerical results (in double precision) give good agreement with the provided theory.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.11-m11168}, url = {http://global-sci.org/intro/article_detail/aamm/58.html} }
TY - JOUR T1 - Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs AU - Shirzadi , Ahmad AU - Ling , Leevan JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 78 EP - 89 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.11-m11168 UR - https://global-sci.org/intro/article_detail/aamm/58.html KW - Local integral equations, meshless methods, radial basis functions, overdetermined systems, solvability, convergence. AB -

This paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial basis function (RBF) kernels generated trial spaces. Local weak-form testings are done with step-functions. It is proved that subject to sufficiently many appropriate testings, solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed. Moreover, an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation. Numerical results (in double precision) give good agreement with the provided theory.

Ahmad Shirzadi & Leevan Ling. (1970). Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs. Advances in Applied Mathematics and Mechanics. 5 (1). 78-89. doi:10.4208/aamm.11-m11168
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