Title: Solving delay differential equations through RBF collocation,
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.