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TWO NEW PHASE-FITTED SYMPLECTIC PARTITIONED RUNGE–KUTTA METHODS

Department of International Trade, Technological Educational Institute of Western Macedonia at Kastoria, P. O. Box 30, GR-521 00, Kastoria, Greece

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Z. KALOGIRATOU

Department of Informatics and Computer Technology, Technological Educational Institute of Western Macedonia at Kastoria, P. O. Box 30, GR-521 00, Kastoria, Greece

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, and

T. E. SIMOS

Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100 Tripolis, Greece

Corresponding author.

Active Member of the European Academy of Sciences and the European Academy of Sciences and Arts. Corresponding Member of the European Academy of Arts, Sciences and Humanities.

Current address: Dr. T. E. Simos, 10 Konitsis Street, Amfithea-Paleon Faliron, GR-175 64 Athens, Greece, Tel.: 0030 210 94 20 091.

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https://doi.org/10.1142/S0129183111016932Cited by:42 (Source: Crossref)

Abstract

New symplectic Partitioned Runge–Kutta (SPRK) methods with phase-lag of order infinity are derived in this paper. Specifically two new symplectic methods are constructed with second and third algebraic order. The methods are tested on the numerical integration of Hamiltonian problems and on the estimation of the eigenvalues of the Schrödinger equation.

Keywords:

PACS: 02.60, 02.70.Bf, 95.10.Ce, 95.10.Eg, 95.75.Pq

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