Solving delay differential equations through RBF collocation

TL;DR

This paper introduces a simple, accurate RBF collocation method for solving delay differential equations, leveraging smooth RBFs and adaptive support to outperform existing schemes.

Contribution

It presents a novel, easy-to-implement RBF collocation approach with adaptive support for efficiently solving DDEs, demonstrating superior performance.

Findings

High accuracy over scattered data points

Effective support adaptivity improves solutions

Outperforms existing numerical schemes

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.