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Preprint 753-2002
Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability
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Author(s) : Anton Arnold , Matthias Ehrhardt , Ivan Sofronov
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 753-2002
- 65M12 Stability and convergence of numerical methods
- 35Q40 Equations from quantum mechanics
- 45K05 Integro-partial differential equations
As a remedy we construct approximate TBCs with a kernel having the form of a finite sum-of-exponentials, which can be evaluated in a very efficient recursion. We prove stability of the resulting initial-boundary value scheme, give error estimates for the considered approximation of the boundary condition, and illustrate the efficiency of the proposed method on several examples.
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