Time Multipoint Nonlocal Problem for a Stochastic Schrödinger Equation

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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.