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

Ting-On Kwok & Leevan Ling

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

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-1-367, author = {Kwok , Ting-On and Ling , Leevan}, 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 - Kwok , Ting-On AU - Ling , Leevan JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 367 EP - 382 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aamm/8375.html KW - Radial basis function, adaptive greedy algorithm, asymmetric collocation, Kansa's method, 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.

Kwok , Ting-On and Ling , Leevan. (2009). 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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