Biomedical subjects

T E Simos

Publications and source records attributed to T E Simos.

7 recordsLinked to original sources

PubMed2003

Exponentially fitted symplectic integrator.

In this paper a procedure for constructing efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the exponential fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge-Kutta-Nyström second-order algebraic exponentially fitted method is developed. We give explicitly the symplecticness conditions for the modified Runge-Kutta-Nyström method. We also give the exponential fitting and trigonometric fitting conditions. Numerical results indicate that the present method is much more efficient than the "classical" symplectic Runge-Kutta-Nyström second-order algebraic method introduced by M.P. Calvo and J.M. Sanz-Serna [J. Sci. Comput. (USA) 14, 1237 (1993)]. We note that the present procedure is appropriate for all near-unimodal systems.

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PubMed2002

P-stable eighth algebraic order methods for the numerical solution of the Schrödinger equation.

A P-stable method of algebraic order eight for the approximate numerical integration of the Schrödinger equation is developed in this paper. Since the method is P-stable (i.e. its interval of periodicity is equal to (0, infinity)), large step sizes for the numerical integration can be used. Based on this new method and on a sixth algebraic order P-stable method developed by Simos (Phys. Scripta 55 (1997) 644-650), a new variable step method is obtained. Numerical results presented for the phase-shift problem of the radial Schrödinger equation and for the coupled differential equations arising from the Schrödinger equation show the efficiency of the developed method.

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PubMed2001

On variable-step methods for the numerical solution of Schrödinger equation and related problems.

In this paper we present a review for the construction of variable-step methods for the numerical integration of the Schrödinger equation. Phase-lag and stability are investigated. The methods are variable-step because of a simple natural error control mechanism. Numerical results obtained for coupled differential equations arising from the Schrödinger equation and for the wave equation show the validity of the approach presented.

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PubMed2001

New insights in the development of Numerov-type methods with minimal phase-lag for the numerical solution of the Schrödinger equation.

Explicit Numerov-type methods with minimal phase-lag are developed in this paper. These methods are of algebraic order five and have phase-lag order eight and ten. The methods have new features; namely that they are dissipative, i.e. they are not symmetric and they have no interval of periodicity. Numerical illustrations using (i) the radial Schrödinger equation and (ii) coupled differential equations arising from the Schrödinger equation, indicate that these new methods are more efficient than older ones. It is seen that the property of the phase-lag is more important than the non-empty interval of periodicity in constructing numerical methods for the solution of the Schrödinger equations and related problems.

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PubMed2001

Dissipative exponentially-fitted methods for the numerical solution of the Schrödinger equation.

The first dissipative exponentially fitted method for the numerical integration of the Schrödinger equation is developed in this paper. The technique presented is a nonsymmetric multistep (dissipative) method. An application to the bound-states problem and the resonance problem of the radial Schrödinger equation indicates that the new method is more efficient than the classical dissipative method and other well-known methods. Based on the new method and the method of Raptis and Allison (Comput. Phys. Commun. 14 (1978) 1-5) a new variable-step method is obtained. The application of the new variable-step method to the coupled differential equations arising from the Schrödinger equation indicates the power of the new approach.

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PubMed2001

A modified Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems.

A modified Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems is developed in this paper. This new modified method is based on the classical Runge-Kutta method of algebraic order four. The numerical results indicate that this new method is more efficient for the numerical solution of the Schrödinger equation and related problems than the well known classical Runge-Kutta method of algebraic order four.

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PubMedDate not supplied

A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation.

A dissipative exponentially fitted method is constructed in this paper for the numerical integration of the Schrödinger equation. We note that the present method is a nonsymmetric multistep method (dissipative method) An application to the bound-states problem and the resonance problem of the radial Schrödinger equation indicates that the new method is more efficient (i.e. more accurate and more rapid) than the classical dissipative method and other well-known methods. Based on the new method and the method of Raptis and Allison(19) a new variable-step method is obtained. The application of the new variable-step method to the coupled differential equations arising from the Schrödinger equation indicates the efficiency of the new approach.

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