We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
THE STABILITY OF THE PARAMETRIC CAUCHY PROBLEM OF INITIAL-VALUE ORDINARY DIFFERENTIAL EQUATIONS REVISITED.
- Authors
MANSOUR, M. AIT; LAHRACHE, J.; EL AYOUBI, A.
- Abstract
In this paper, given a function f: IxV → ℝm, where V is an open subset of ℝm, x0 ∈ V, and I = [0, T] is the interval of interest, we consider the Cauchy ordinary differential equation initial-value problem ...(f, x0) = f(t, x(t)), x(0) = x0. We first present a new quantitative stability result under a partial and/or global variation of the data of the problem by involving exact and/or approximate fixed points for which we apply Lim's Lemma either in its exact format or in its very recent approximate version. Our main result is then applied to parametric linear control systems. Finally, we demonstrate that our treatment is coherent with the management of perturbations generated in the classic one-step numerical method. A numerical example written in Scilab 6.1 illustrates the obtained stability.
- Subjects
CAUCHY problem; DIFFERENTIAL equations; PARAMETRIC equations; LAMMA language; BOREL subsets
- Publication
Journal of Applied & Numerical Optimization, 2023, Vol 5, Issue 1, p111
- ISSN
2562-5527
- Publication type
Article
- DOI
10.23952/jano.5.2023.1.07