Solving delay differential equations through RBF collocation Articles uri icon

publication date

  • April 2009

start page

  • 257

end page

  • 272


  • 2


  • 1

International Standard Serial Number (ISSN)

  • 2070-0733

Electronic International Standard Serial Number (EISSN)

  • 2075-1354


  • 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.


  • meshless method; delay differential equations; radial basis function; multiquadric; adaptive collocation