Numerical approaches for state-dependent neutral delay equations with discontinuities
Nicola Guglielmi and Ernst Hairer
Abstract.
This article presents two regularization techniques for systems of
state-dependent neutral delay differential equations which have a
discontinuity in the derivative of the solution at the initial point. Such problems have
a rich dynamics and besides classical solutions
can have weak solutions in the sense of Utkin.
Both of the presented
techniques permit the numerical solution of such problems with
the code RADAR5, which is designed to compute classical solutions
of stiff and differential-algebraic
(state-dependent) delay equations.
Key Words.
Neutral delay equation, discontinuity, weak solution (Utkin), regularization, asymptotic expansion, implicit Runge--Kutta method.