Regularization of Neutral Delay Differential Equations with Several Delays |
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Authors: | Nicola Guglielmi Ernst Hairer |
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Institution: | 1. Dipartimento di Matematica Pura e Applicata, Università dell’Aquila, via Vetoio (Coppito), 67010, ?L’Aquila, Italy 2. Section de Mathématiques, Université de Genève, 1211, Geneva 24, Switzerland
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Abstract: | For neutral delay differential equations the right-hand side can be multi-valued, when one or several delayed arguments cross a breaking point. This article studies a regularization via a singularly perturbed problem, which smooths the vector field and removes the discontinuities in the derivative of the solution. A low-dimensional dynamical system is presented, which characterizes the kind of generalized solution that is approximated. For the case that the solution of the regularized problem has high frequency oscillations around a codimension-2 weak solution of the original problem, a new stabilizing regularization is proposed and analyzed. |
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