A Fully-Discrete Spectral Method for Delay-Differential Equations

In this paper a new Lanczos-tau method for solving linear functional differential equations is introduced. The scheme has infinite order of accuracy both in time and in the delayed argument. The high accuracy in time is obtained without increasing the computational work and memory space which is needed for a one-step explicit difference scheme. The article demonstrates how to implement the algorithm in a robust and efficient manner and to treat problems with piecewise continuous initial function. Numerical results illustrating the behavior of the method when faced with difficult problems are presented and the numerical results are compared to those obtained by using two other methods.