Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions |
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Authors: | G A Panopoulos Z A Anastassi and T E Simos |
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Institution: | (1) Laboratory of Computer Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, 22 100 Tripolis, Greece;(2) 26 Menelaou Street, Amfithea—Paleon Faliron, 175 64 Athens, Greece |
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Abstract: | In this paper, 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 Schr?dinger 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.
T. E. Simos—Highly Cited Researcher, Active Member of the European Academy of Sciences and Arts. |
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Keywords: | Schr?dinger equation Orbital problems Phase-lag Initial value problems Oscillating solution Symmetric Multistep Implicit |
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