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 - <p style="text-align: justify;">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&#39;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.</p>