Showing papers by "Th. Monovasilis published in 2011"

Two new phase-fitted symplectic partitioned runge–kutta methods

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 Schrodinger equation.

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

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 Schrodinger equation.

A Diagonally Implicit Symplectic Runge‐Kutta Method with Minimum Phase‐lag

Abstract: The numerical integration of Hamiltonian systems is considered in this paper. A diagonally implicit Symplectic Runge‐Kutta method with five stages, fourth algebraic order and sixth phase‐lag order is presented.

A Trigonometrically Fitted Symplectic Runge‐Kutta‐Nyström Method

Abstract: In this work we consider Trigonometrically Fitted Symplectic Runge Kutta Nystrom methods. We present a new Trigonometrically fitted symplectic three stage method with algebraic order two.