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Stability analysis of difference schemes for variable coefficient Schrödinger type equations. (English) Zbl 0646.65089
The stability or conditional stability, respectively, are established for the solution of initial-boundary value problems for a linear equation with complex-valued coefficients. Modified by some appropriately chosen artificial dissipation, the explicit Euler method is proven to be conditionally stable for a purely imaginary leading coefficient, too.
Reviewer: G.Lippold
MSC:
65Z05Applications of numerical analysis to physics
65N12Stability and convergence of numerical methods (BVP of PDE)
35Q99PDE of mathematical physics and other areas
81Q05Closed and approximate solutions to quantum-mechanical equations