Open AccessA stochastic controlled Schroedinger equation: convergence and robust stability for numerical solutions
Author(s) -
Cutberto Romero-Meléndez,
David Chelo
Publication year - 2021
Publication title -
cybernetics and physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 8
eISSN - 2226-4116
pISSN - 2223-7038
DOI - 10.35470/2226-4116-2021-10-3-178-184
Subject(s) - mathematics , stability (learning theory) , exponential stability , convergence (economics) , operator (biology) , schrödinger equation , diffusion equation , mathematical analysis , computer science , physics , biochemistry , chemistry , repressor , quantum mechanics , nonlinear system , machine learning , transcription factor , economics , gene , economic growth , economy , service (business)
In this paper we study the stochastic stability of numerical solutions of a stochastic controlled Schr¨odinger equation. We investigate the boundedness in second moment, the convergence and the stability of the zero solution for this equation, using two new definitions of almost sure exponential robust stability and asymptotic stability, for the Euler-Maruyama numerical scheme. Considering that the diffusion term is controlled, by using the method of Lyapunov functions and the corresponding diffusion operator associated, we apply techniques of X. Mao and A. Tsoi for achieve our task. Finally,we illustrate this method with a problem in Nuclear Magnetic Resonance (NMR).