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Error estimate of fourth-order compact scheme for linear Schrödinger equations. (English) Zbl 1208.65130
A fourth-order compact difference scheme is proposed for solving multidimensional linear Schrödinger equations with periodic boundary conditions. Based on a coupled system of the initial-boundary value problem a novel technique of $H^2$ error analysis is introduced to analyze the compact difference method. With an asymptotic expansion of the numerical solution, two higher-order stable approximations are obtained. Theoretical results are supported by numerical tests.

##### MSC:
 65M06 Finite difference methods (IVP of PDE) 65M12 Stability and convergence of numerical methods (IVP of PDE) 65M15 Error bounds (IVP of PDE)
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