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 classicalsolutions 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.
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