Path-regularization of linear neutral delay differential equations with several delays

• Nicola Guglielmi ^[2] ; Ernst Hairer ^[1]
  1. [1] Université de Genève

     Université de Genève

     Genève, Suiza

     
  2. [2] Università dell’Aquila, Italy
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 292, Nº 1 (15 January 2016), 2016, págs. 785-794
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.12.028
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• Resumen

  • For differential equations with discontinuous right-hand side and, in particular, for neutral delay equations it may happen that classical solutions do no exist beyond a certain time instant. In this situation, it is common to consider weak solutions of Utkin (Filippov) type. This article extends the concept of weak solutions and proposes a new regularization which eliminates the discontinuities. Codimension-1 and codimension-2 weak solutions are considered. Numerical experiments show the advantages of the new regularization