Volume 1, Issue 3
On Convergence of a Least-Squares Kansa's Method for the Modified Helmholtz Equations

Ting-On Kwok & Leevan Ling

DOI:

Adv. Appl. Math. Mech., 1 (2009), pp. 367-382.

Published online: 2009-01

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  • Abstract

We analyze a least-squares  asymmetric radial basis function collocation method for solving the modified Helmholtz equations. In the theoretical part, we proved the convergence of the proposed method providing that the collocation points are sufficiently dense. For numerical verification, direct solver and a subspace selection process for the trial space (the so-called adaptive greedy algorithm) is employed, respectively, for small and large scale problems.

  • Keywords

Radial basis function adaptive greedy algorithm asymmetric collocation Kansa's method convergence analysis

  • AMS Subject Headings

35J25 65N12 65N15 65N35

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COPYRIGHT: © Global Science Press

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@Article{AAMM-1-367, author = {Ting-On Kwok and Leevan Ling}, title = {On Convergence of a Least-Squares Kansa's Method for the Modified Helmholtz Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {3}, pages = {367--382}, abstract = {

We analyze a least-squares  asymmetric radial basis function collocation method for solving the modified Helmholtz equations. In the theoretical part, we proved the convergence of the proposed method providing that the collocation points are sufficiently dense. For numerical verification, direct solver and a subspace selection process for the trial space (the so-called adaptive greedy algorithm) is employed, respectively, for small and large scale problems.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/8375.html} }
TY - JOUR T1 - On Convergence of a Least-Squares Kansa's Method for the Modified Helmholtz Equations AU - Ting-On Kwok & Leevan Ling JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 367 EP - 382 PY - 2009 DA - 2009/01 SN - 1 DO - http://dor.org/ UR - https://global-sci.org/intro/aamm/8375.html KW - Radial basis function KW - adaptive greedy algorithm KW - asymmetric collocation KW - Kansa's method KW - convergence analysis AB -

We analyze a least-squares  asymmetric radial basis function collocation method for solving the modified Helmholtz equations. In the theoretical part, we proved the convergence of the proposed method providing that the collocation points are sufficiently dense. For numerical verification, direct solver and a subspace selection process for the trial space (the so-called adaptive greedy algorithm) is employed, respectively, for small and large scale problems.

Ting-On Kwok & Leevan Ling. (1970). On Convergence of a Least-Squares Kansa's Method for the Modified Helmholtz Equations. Advances in Applied Mathematics and Mechanics. 1 (3). 367-382. doi:
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