A spectral collocation method for mixed functional differential equations

摘要

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.