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The numerical integration of neutral functional-differential equations by fully implicit one-step methods. (English) Zbl 0830.65079
This paper deals with fully implicit one-step methods for the numerical solution of neutral functional-differential equations (NFDEs) and develops a divided difference representation of these formulas. The authors also discuss how to estimate the local discretization error in an efficient way by comparing two approximations of successive orders.
The predictor-corrector implementation of fully implicit one-step methods is described in a general context of NFDEs, with additional details of implementation for systems of neutral delay differential equations, for Volterra integro-differential equations, and for stiff delay differential equations. If the delay equation is stiff the system of the resulting nonlinear equations is solved by a variant of Newton’s method. Some numerical experiments are presented and discussed.

##### MSC:
 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L05 Numerical methods for initial value problems 65L12 Finite difference and finite volume methods for ordinary differential equations 65R20 Numerical methods for integral equations 65L70 Error bounds for numerical methods for ordinary differential equations 34K05 General theory of functional-differential equations 34E13 Multiple scale methods for ordinary differential equations 45J05 Integro-ordinary differential equations
DELSOL
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