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

作者：Guglielmi Nicola^*; Hairer Ernst

来源：Journal of Computational and Applied Mathematics, 2016, 292: 785-794.

DOI：10.1016/j.cam.2014.12.028

• Neutral delay equations
• Weak solutions
• Discontinuous differential equations
• Path-regularization
• Stability

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.

• 出版日期2016-1-15