TY - JOUR
T1 - Time Multipoint Nonlocal Problem for a Stochastic Schrödinger Equation
AU - Pettersson , Roger
AU - Sirma , Ali
AU - Aydin , Tarkan
JO - Journal of Computational Mathematics
VL - 2
SP - 369
EP - 393
PY - 2024
DA - 2024/11
SN - 43
DO - http://doi.org/10.4208/jcm.2210-m2022-0057
UR - https://global-sci.org/intro/article_detail/jcm/23542.html
KW - Time nonlocal problem, Mild solution, Cylindrical Wiener process, Time discretization, Abstract time-dependent stochastic Schrödinger equation, Euler-Maruyama method.
AB - <p style="text-align: justify;">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.</p>