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Padé and upwinding finite difference schemes for the quantum mechanical equation of motion. (English) Zbl 0744.65093

This paper presents a systematic approach to search for a two-level six- point finite difference of Padé type for the numerical solution of the quantum mechanical equation of motion. Convergence and stability, properties are also analyzed. It is shown that Padé schemes are unconditionally stable.

MSC:

65Z05 Applications to the sciences
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q40 PDEs in connection with quantum mechanics
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References:

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[2] Numerical Solutions of Partial Differential Equations: Finite Difference Methods, 3rd edn, Oxford University Press, 1985.
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[4] Chattaraj, J. Comput. Phys. 72 pp 504– (1987)
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