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A new explicit hybrid four-step method with vanished phase-lag and its derivatives |
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| Authors: | T. E. Simos |
| Affiliation: | 1. Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia 2. Laboratory of Computational Sciences, Department of Informatics and Telecommunications, Faculty of Economy, Management and Informatics, University of Peloponnese, 221 00, Tripoli, Greece 3. 10 Konitsis Street, Amfithea - Paleon Faliron, 175 64, Athens, Greece |
| Abstract: | A hybrid explicit sixth algebraic order four-step method with phase-lag and its first, second and third derivatives vanished is obtained in this paper. We present the development of the new method, its comparative error analysis and its stability analysis. The resonance problem of the Schrödinger equation, is used in order to study the efficiency of the new developed method. After the presentation of the theoretical and the computational results it is easy to see that the new constructed method is more efficient than other well known methods for the approximate solution of the Schrödinger equation and related initial-value or boundary-value problems with periodic and/or oscillating solutions. |
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