On a step method and a propagation of discontinuity. (English) Zbl 1438.34219
Summary: In this paper, we analyze how to compute discontinuous solutions for functional differential equations, looking at an approach which allows to study simultaneously continuous and discontinuous solutions. We focus our attention on the integral representation of solutions and we justify the applicability of such an approach. In particular, we improve the step method in such a way to solve a problem of vanishing discontinuity points. Our solutions are considered as regulated functions.
MSC:
| 34K05 | General theory of functional-differential equations |
| 26A42 | Integrals of Riemann, Stieltjes and Lebesgue type |
| 65L03 | Numerical methods for functional-differential equations |
Keywords:
regulated function; discontinuous function; retarded differential equation; delay; Kurzweil-Stieltjes integral; breaking pointsReferences:
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