An explicit eighth-order method with minimal phase-lag for accurate computations of eigenvalues,resonances and phase shifts |
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| Affiliation: | 1. School of Engineering, Department of Civil Engineering, Demokritus University of Thrace, GR-671 00, Xanthi, Greece;2. Department of Sciences, Technical University of Crete, Kounoupidiana, 73 100 Hania, Crete, Greece;1. Vilnius University, Institute of Applied Research, Sauletekio 10, 10223 Vilnius, Lithuania;2. Vilnius University, Faculty of Mathematics and Informatics, Didlaukio 47, LT-08303 Vilnius, Lithuania;1. School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology, Xi’an 710021, China;2. School of Material Science and Engineering, Shaanxi University of Science and Technology, Xi’an 710021, China;1. Materials Science & Technology Division, National Institute for Interdisciplinary Science & Technology, Trivandrum 695019, India;2. Materials Physics and Microelectronics Lab., Department of Electrical Engineering, University of Oulu, 90014 Finland;1. Faculty of Health Sciences University of Ljubljana, Midwifery Department, Zdravstvena pot 5, 1000 Ljubljana, Slovenia;2. Jessenius Faculty of Medicine in Martin, Comenius University in Bratislava, Department of Midwifery, Malá Hora 5, 036 01 Martin, Slovakia;3. Faculty of Medicine Masaryk University, Midwifery Department, Komenského nám. 2, 643 00 Brno, Czech Republic |
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| Abstract: | A new explicit hybrid eighth algebraic order two-step method with phase-lag of order ten is developed for computing eigenvalues, resonances and phase shifts of the one-dimensional Schrödinger equation and coupled differential equations arising from the Schrödinger equation. Based on this new method and on the method developed recently by Simos we obtain a new variable-step procedure for the numerical integration of the Schrödinger equation. Numerical results obtained for the integration of the resonance problem for the well known case of the Woods-Saxon potential, for the integration of the eigenvalue problem for the well known case of the Morse potential and for the integration of coupled differential equations show that this new method is better than other variable-step methods. |
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