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On the numerical solution of fractional Schrödinger differential equations with the Dirichlet condition. (English) Zbl 1255.65156
Summary: The first and second orders of accuracy difference schemes for the mixed problem for the multidimensional fractional Schrödinger differential equation with dependent coefficients are considered. Stability estimates for solutions of these difference schemes are obtained. Numerical methods are proposed for solving the one-dimensional fractional Schrödinger differential equation with Dirichlet condition in the space variable.
MSC:
65M06Finite difference methods (IVP of PDE)
35R11Fractional partial differential equations