Time Multipoint Nonlocal Problem for a Stochastic Schrödinger Equation (Journal of Computational Mathematics, 2024)
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 futurevalues. 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, issuggested as a numerical solution. Convergence rate for the solution of the differencescheme is established. The theoretical statements for the solution of this difference schemeis 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.