Solving Delay Differential Equations Through RBF Collocation (Advances in Applied Mathematics and Mechanics, 2018)
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 allowfor a large accuracy over a scattered and relatively small discretization support.Hardy's multiquadric is chosen as RBF and combined with the Residual SubsamplingAlgorithm of Driscoll and Heryudono for support adaptivity. The performanceof the method is very satisfactory, as demonstrated over a cross-section ofbenchmark DDEs, and by comparison with existing general-purpose and specializednumerical schemes for DDEs.