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Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions. (English) Zbl 1198.81099

Summary: We present two optimized eight-step symmetric implicit methods with phase-lag order ten and infinite (phase-fitted). The methods are constructed to solve numerically the radial time-independent Schrödinger equation with the use of the Woods-Saxon potential. They can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the two new methods to some recently constructed optimized methods from the literature. We measure the efficiency of the methods and conclude that the new method with infinite order of phase-lag is the most efficient of all the compared methods and for all the problems solved.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81V45 Atomic physics
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)

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DAETS; SCHOL; VFGEN; Maple; pythNon
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References:

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