Solving delay differential equations through RBF collocation
It provides a general, easy-to-code numerical method for solving delay differential equations, which are important in various scientific fields.
The paper proposes a numerical method using radial basis function collocation for solving delay differential equations, achieving high accuracy with small scattered support and demonstrating satisfactory performance on benchmarks compared to existing methods.
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.