A spectral collocation method for mixed functional differential equations

We propose and investigate a Chebyshev spectral collocation method for solving mixed functional differential equations. One can usually not solve these equations analytically, and hence one must employef numerical methods. Our method is for boundary value problems which include delay and advance terms in the solution or a derivative. Even though, in general, solutions are not very smooth, spectral collocation methods are well suited for these types of problems as they allow easy and accurate evaluation of the approximated solution at points which are not grid points. We present numerical results and examine smoothness related convergence behaviour. Crown Copyright (c) 2020 Published by Elsevier B.V. on behalf of IMACS. All rights reserved.

Automated summary

A Chebyshev spectral collocation method is proposed for solving mixed functional differential equations involving delay, advance terms, or derivatives in boundary value problems. Despite the generally not very smooth solutions, the method allows for accurate evaluation of approximated solutions at points not on the grid. The study presents numerical results and examines convergence behavior related to smoothness.