Journal ArticleDOI
A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equation
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TLDR
In this article, an explicit eighth algebraic order Bessel and Neumann fitted method is developed for the numerical solution of the Schrodinger equation, which is more efficient than other well known methods.Abstract:
An explicit eighth algebraic order Bessel and Neumann fitted method is developed in this paper for the numerical solution of the Schrodinger equation. The new method has free parameters which are defined in order the method is fitted to spherical Bessel and Neumann functions. A variable-step procedure is obtained based on the newly developed method and the method of Simos [17]. Numerical illustrations based on the numerical solution of the radial Schrodinger equation and of coupled differential equations arising from the Schrodinger equation indicate that this new approach is more efficient than other well known methods.read more
Citations
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Solving Ordinary Differential Equations
TL;DR: The variable-order Adams method (SIVA/DIVA) package as discussed by the authors is a collection of subroutines for solution of non-stiff ODEs.
Journal ArticleDOI
Exponentially and Trigonometrically Fitted Methods for the Solution of the Schrödinger Equation
TL;DR: In this paper, the authors compare the efficiency of exponential and trigonometrically fitted methods for solving the one-dimensional Schrodinger equation with constant coefficients, and present the error analysis of the above two approaches.
Journal ArticleDOI
High order closed Newton–Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation
TL;DR: The closed Newton–Cotes formulae are studied and written as symplectic multilayer structures and trigonometrically-fitted symplectic methods are developed and applied to the well-known radial Schrodinger equation to investigate the efficiency of the proposed method.
High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrodinger equation
TL;DR: In this paper, the authors investigated the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, and symplectic integrators and the efficient integration of the Schrodinger equation.
Journal ArticleDOI
Multiderivative methods of eighth algebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation
Damianos P. Sakas,T. E. Simos +1 more
TL;DR: In this article, a multiderivative method with minimal phase-lag was proposed for the numerical solution of the one-dimensional Schrodinger equation, which uses derivatives of order two, four or six.
References
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Solving Ordinary Differential Equations
TL;DR: The variable-order Adams method (SIVA/DIVA) package as discussed by the authors is a collection of subroutines for solution of non-stiff ODEs.
Journal ArticleDOI
Exponential-fitting methods for the numerical solution of the schrodinger equation
A. D. Raptis,A.C. Allison +1 more
TL;DR: The Chebyshevian multi-step theory of Lyche has been applied to the numerical solution of the radial form of the Schrodinger equation as mentioned in this paper, and significant improvements over previously reported approaches are found.
Journal ArticleDOI
The numerical solution of coupled differential equations arising from the Schrödinger equation
TL;DR: In this paper, several step-by-step methods for the numerical solution of coupled differential equations are given and compared under realistic circumstances, and a variant of the Numerov method is found to be the most efficient.
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