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Volume 43, Issue 2
Time Multipoint Nonlocal Problem for a Stochastic Schrödinger Equation

Roger Pettersson, Ali Sirma & Tarkan Aydin

DOI: 10.4208/jcm.2210-m2022-0057

J. Comp. Math., 43 (2025), pp. 369-393.

Published online: 2024-11

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  • 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.

  • Keywords

Time nonlocal problem, Mild solution, Cylindrical Wiener process, Time discretization, Abstract time-dependent stochastic Schrödinger equation, Euler-Maruyama method.

  • AMS Subject Headings

60H20, 60H35, 35J10, 65H10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-43-369, author = {Pettersson , RogerSirma , Ali and Aydin , Tarkan}, title = {Time Multipoint Nonlocal Problem for a Stochastic Schrödinger Equation}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {43}, number = {2}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2210-m2022-0057}, url = {http://global-sci.org/intro/article_detail/jcm/23542.html} }
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 -

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.

Pettersson , RogerSirma , Ali and Aydin , Tarkan. (2024). Time Multipoint Nonlocal Problem for a Stochastic Schrödinger Equation. Journal of Computational Mathematics. 43 (2). 369-393. doi:10.4208/jcm.2210-m2022-0057
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