Solving Delay Differential Equations through RBF Collocation
Francisco Bernal 1*, Gail Gutierrez 21 Institute for Scientific Computing, Technical University of Dresden 01062 Dresden, Germany.
2 Cir 1 No. 73-34, Instituto de Energia y Termodinamica, Universidad Pontificia Bolivariana, Medellin, Colombia.
Received 23 October 2008; Accepted (in revised version) 27 December 2008
Ageneral 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.AMS subject classifications: 34-04, 65L99
Key words: Meshless method, delay differential equations, radial basis function, multiquadric, adaptive collocation.
Email: fco email@example.com (F. Bernal), firstname.lastname@example.org (G. Gutierrez)