A Review of DDE Methods
This chapter starts with a brief historical excursus of the early methods used for the numerical solution of DDEs. It then considers general formulation and convergence results for discrete and continuous methods for ODEs, which constitute the basis for the standard approach that is extensively treated in this book for solving DDEs numerically. Although the book focuses on the class of continuous Runge-Kutta methods, more general multistep methods are considered for the sake of completeness. The main features of the standard approach for DDEs and for neutral DDEs are introduced and discussed. The classical Bellman method of steps and waveform relaxation methods are described. Another innovative approach based on the transformation of the DDE into an abstract Cauchy problem is solved by a standard ODE method.
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