Year: 2025
Author: Roger Pettersson, Ali Sirma, Tarkan Aydin
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 2 : pp. 369–393
Abstract
A time multipoint nonlocal problem for a Schrödinger equation driven by a cylindrical $Q$-Wiener process is presented. The initial value depends on a finite number of future values. Existence and uniqueness of a solution formulated as a mild solution is obtained. A single-step implicit Euler-Maruyama difference scheme, a Rothe-Maruyama scheme, is suggested as a numerical solution. Convergence rate for the solution of the difference scheme is established. The theoretical statements for the solution of this difference scheme is supported by a numerical example.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2210-m2022-0057
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 2 : pp. 369–393
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Time nonlocal problem Mild solution Cylindrical Wiener process Time discretization Abstract time-dependent stochastic Schrödinger equation Euler-Maruyama method.