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Ramos H.,University of Salamanca | Kalogiratou Z.,Technological Educational Institution of Western Macedonia at Kastoria | Monovasilis Th.,Technological Educational Institute of West Macedonia | Simos T.E.,University of Peloponnese | Simos T.E.,King Saud University
AIP Conference Proceedings | Year: 2015

In this paper, a new optimized implicit two-step hybrid block method with trigonometrically adapted features is presented for the integration of general second-order initial value problems whose solutions are oscillatory. Numerical experiments reveal the good performance of the new method for solving these kinds of problems, in comparison with other methods in the literature. © 2015 AIP Publishing LLC. Source


Kalogiratou Z.,Technological Educational Institution of Western Macedonia at Kastoria | Monovasilis T.,Technological Educational Institute of West Macedonia | Psihoyios G.,University of Peloponnese | Simos T.E.,University of Peloponnese | Simos T.E.,King Saud University
Physics Reports | Year: 2014

In this work we review single step methods of the Runge-Kutta type with special properties. Among them are methods specially tuned to integrate problems that exhibit a pronounced oscillatory character and such problems arise often in celestial mechanics and quantum mechanics. Symplectic methods, exponentially and trigonometrically fitted methods, minimum phase-lag and phase-fitted methods are presented. These are Runge-Kutta, Runge-Kutta-Nyström and Partitioned Runge-Kutta methods. The theory of constructing such methods is given as well as several specific methods. In order to present the performance of the methods we have tested 58 methods from all categories. We consider the two dimensional harmonic oscillator, the two body problem, the pendulum problem and the orbital problem studied by Stiefel and Bettis. Also we have tested the methods on the computation of the eigenvalues of the one dimensional time independent Schrödinger equation with the harmonic oscillator, the doubly anharmonic oscillator and the exponential potentials. © 2013 Elsevier B.V.. Source


Monovasilis T.,Technological Educational Institution of Western Macedonia at Kastoria
Journal of Mathematical Chemistry | Year: 2012

In this work we consider explicit symplectic partitioned Runge-Kutta methods with five stages for problems with separable Hamiltonian. We construct three new methods, one with constant coefficients of eight phase-lag order and two phase-fitted methods. © 2012 Springer Science+Business Media, LLC. Source


Kalogiratou Z.,Technological Educational Institution of Western Macedonia at Kastoria | Monovasilis T.,Technological Educational Institute of West Macedonia | Simos T.E.,King Saud University | Simos T.E.,University of Peloponnese
Computer Physics Communications | Year: 2014

In this work we construct a modified trigonometrically fitted symplectic Runge Kutta Nyström method based on the fourth order five stages method of Calvo and Sanz-Serna (1994). We apply the new method on the numerical integration of the two-dimensional harmonic oscillator, the two-body problem, a perturbed two-body problem and two two-dimensional nonlinear oscillatory Hamiltonian systems. © 2014 Elsevier B.V. Source


Kalogiratou Z.,Technological Educational Institution of Western Macedonia at Kastoria | Monovasilis T.,Technological Educational Institution of Western Macedonia at Kastoria | Simos T.E.,King Saud University | Simos T.E.,Sudan University of Science and Technology
AIP Conference Proceedings | Year: 2012

The numerical integration of Hamiltonian systems is considered in this paper. Diagonally implicit Symplectic Runge-Kutta methods with special properties are presented. The methods developed have six and seven stages algebraic order up to 5th and dispersion order up to 8th. © 2012 American Institute of Physics. Source

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