High Order Scheme for Schrödinger Equation with Discontinuous Potential I: Immersed Interface Method

The immersed interface method is modified to compute Schrodinger equa- tion with discontinuous potential. By building the jump conditions of the solution into the finite difference approximation near the interface, this method can give at least sec- ond order convergence rate for the numerical solution on uniform cartesian grids. The accuracy of this algorithm is tested via several numerical examples. AMS subject classifications: 35R05, 65M06, 81Q05

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