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New P-stable eighth algebraic order exponentially-fitted methods for the numerical integration of the Schrödinger equation. (English) Zbl 1078.65061

Summary: A family of P-stable high algebraic order exponentially-fitted methods for the numerical solution of the Schrödinger equation is developed in this paper. Numerical illustration to the resonance problem of the radial Schrödinger equation indicates that the new proposed methods are generally more efficient than the previously developed exponentially-fitted methods of the same kind.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81-08 Computational methods for problems pertaining to quantum theory
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