Symplectic Partitioned Runge-Kutta Methods for the Numerical Integration of Periodic and Oscillatory Problems

Z. Kalogiratou, Th. Monovasilis and T. E. Simos ()
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Z. Kalogiratou: Technological Educational Institute of Western Macedonia at Kastoria, Department of Informatics and Computer Technology
Th. Monovasilis: Technological Educational Institute of Western Macedonia at Kastoria, Department of International Trade
T. E. Simos: University of Peloponnessos, Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Science and Technology

Chapter Chapter 8 in Recent Advances in Computational and Applied Mathematics, 2011, pp 169-208 from Springer

Abstract: Abstract In this work specially tuned Symplectic Partitioned Runge-Kutta (SPRK) methods have been considered for the numerical integration of problems with periodic or oscillatory solutions. The general framework for constructing exponentially/trigonometrically fitted SPRK methods is given and methods with corresponding order up to fifth have been constructed. The trigonometrically-fitted methods constructed are of two different types, fitting at each stage and Simos’s approach. Also, SPRK methods with minimal phase-lag are derived as well as phase-fitted SPRK methods. The methods are tested on the numerical integration of Kepler’s problem, Stiefel-Bettis problem and the computation of the eigenvalues of the Schrödinger equation.

Keywords: Partitioned-Runge-Kutta methods; Symplecticness; Exponentiall/trigonometricall fitting; Minimum phase-lag; Phase-fitting; Schrödinger equation; Hamiltonian problems; 65L15; 65L06; 65L10; 65P10 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-90-481-9981-5_8

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DOI: 10.1007/978-90-481-9981-5_8

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