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The Numerical Integration of Neutral Functional‐Differential Equations by Fully Implicit One‐Step Methods
Author(s) -
Jackiewicz Z.,
Lo E.
Publication year - 1995
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19950750308
Subject(s) - nonlinear system , mathematics , numerical partial differential equations , differential equation , backward differentiation formula , delay differential equation , runge–kutta methods , numerical stability , explicit and implicit methods , numerical methods for ordinary differential equations , collocation method , numerical analysis , mathematical analysis , ordinary differential equation , physics , quantum mechanics
An algorithm for the numerical solution of neutral functional‐differential equations is described. This algorithm is based on divided difference representation of fully implicit one‐step methods. The resulting systems of nonlinear equations are solved using the predictor‐corrector approach for nonstiff equations and by the modified Newton method for stiff equations. The step control strategy is based on local error estimation by comparing two approximations of successive orders. The details of implementations are described for systems of neutral delay‐differential equations with state dependent delays, for Volterra integro‐differential equations and for stiff delay‐differential equations. The results of some numerical experiments on four test examples are presented and discussed.