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Time Multipoint Nonlocal Problem for a Stochastic Schrödinger Equation
Roger Pettersson, Ali Sirma and Tarkan Aydin

J. Comp. Math. DOI: 10.4208/jcm.2210-m2022-0057

Publication Date : 2024-01-31

  • 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-Maryuama 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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