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Volume 1, Issue 2
Solving Delay Differential Equations Through RBF Collocation

Francisco Bernal & Gail Gutierrez

Adv. Appl. Math. Mech., 1 (2009), pp. 257-272.

Published online: 2009-01

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  • Abstract

A general and easy-to-code numerical method based on radial basis functions (RBFs) collocation is proposed for the solution of delay differential equations (DDEs). It relies on the interpolation properties of infinitely smooth RBFs, which allow for a large accuracy over a scattered and relatively small discretization support. Hardy's multiquadric is chosen as RBF and combined with the Residual Subsampling Algorithm of Driscoll and Heryudono for support adaptivity. The performance of the method is very satisfactory, as demonstrated over a cross-section of benchmark DDEs, and by comparison with existing general-purpose and specialized numerical schemes for DDEs.

  • Keywords

Meshless method, delay differential equations, radial basis function, multiquadric, adaptive collocation.

  • AMS Subject Headings

34-04, 65L99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-1-257, author = {Bernal , Francisco and Gutierrez , Gail}, title = {Solving Delay Differential Equations Through RBF Collocation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {2}, pages = {257--272}, abstract = {

A general and easy-to-code numerical method based on radial basis functions (RBFs) collocation is proposed for the solution of delay differential equations (DDEs). It relies on the interpolation properties of infinitely smooth RBFs, which allow for a large accuracy over a scattered and relatively small discretization support. Hardy's multiquadric is chosen as RBF and combined with the Residual Subsampling Algorithm of Driscoll and Heryudono for support adaptivity. The performance of the method is very satisfactory, as demonstrated over a cross-section of benchmark DDEs, and by comparison with existing general-purpose and specialized numerical schemes for DDEs.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/8368.html} }
TY - JOUR T1 - Solving Delay Differential Equations Through RBF Collocation AU - Bernal , Francisco AU - Gutierrez , Gail JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 257 EP - 272 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aamm/8368.html KW - Meshless method, delay differential equations, radial basis function, multiquadric, adaptive collocation. AB -

A general and easy-to-code numerical method based on radial basis functions (RBFs) collocation is proposed for the solution of delay differential equations (DDEs). It relies on the interpolation properties of infinitely smooth RBFs, which allow for a large accuracy over a scattered and relatively small discretization support. Hardy's multiquadric is chosen as RBF and combined with the Residual Subsampling Algorithm of Driscoll and Heryudono for support adaptivity. The performance of the method is very satisfactory, as demonstrated over a cross-section of benchmark DDEs, and by comparison with existing general-purpose and specialized numerical schemes for DDEs.

Bernal , Francisco and Gutierrez , Gail. (2009). Solving Delay Differential Equations Through RBF Collocation. Advances in Applied Mathematics and Mechanics. 1 (2). 257-272. doi:
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