Title :
Fully implicit one-step methods for neutral functional-differential equations
Author_Institution :
Dept. of Math., Arizona State Univ., Tempe, AZ, USA
Abstract :
The author discusses the class of fully implicit one-step methods of any order for the numerical solution of neutral functional-differential equations. For judicious choices of the parameters these methods are NP-stable, which means that the numerical approximation to the solution Y of the linear test equation y´=ay(t)+by(t-d) + cy´(t-d), t⩾0, is bounded whenever Y is bounded. This property is an analogue of A-stability of ordinary differential equations. The local discretization error of these methods can be estimated by comparing two approximations of successive orders. This can be done in a very efficient way, and these methods can be implemented in variable-step mode with a step-changing strategy based on this estimate. Numerical results are presented that illustrate the high potential of fully implicit formulas
Keywords :
differential equations; function approximation; numerical analysis; NP-stable; fully implicit one-step methods; neutral functional-differential equations; numerical approximation; step-changing strategy; variable-step mode; Convergence; Delay; Differential equations; Lagrangian functions; Mathematics; Polynomials; Stability; Terminology; Testing; US Government;
Conference_Titel :
Decision and Control, 1988., Proceedings of the 27th IEEE Conference on
Conference_Location :
Austin, TX
DOI :
10.1109/CDC.1988.194424