A family of two-stage two-step methods for the numerical integration of the Schrödinger equation and related IVPs with oscillating solution

“…Paternoster [5] presents the overview of recent literature of EF methods. As for mathematical chemistry and physics, Anastassi and Simos [6] proposed EF methods for the numerical integration of the Schrödinger equation and related initial value problems with oscillating solution. The similarities and differences between NSFD and EF methods are discussed by Erdogan [7] and Gurski [8].…”

Section: Exponentially Fitted Finite Difference Formulationmentioning

confidence: 99%

Exponentially Fitted Finite Difference Schemes for Reaction-Diffusion Equations

Erdoğan

Akarbulut

Tan

2016

MCA

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Abstract:The purpose of this work is to introduce a new kind of finite difference formulation inspired from Fourier analysis, for reaction-diffusion equations. Compared to classical schemes, the proposed scheme is much more accurate and has interesting stability properties. Convergence properties and stability of the scheme are discussed. Numerical examples are provided to show better performance of the method, compared with other existing methods in the literature.

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“…Large research on the algorithmic development of numerical methods for the solution of the Schrödinger equation has been done in the last decades. The aim and scope of this research is the construction of fast and reliable algorithms for the solution of the Schrödinger equation and related problems (see for example [2,3,4,5]). Mathematical models in theoretical physics and chemistry, material sciences, quantum mechanics and quantum chemistry, electronics etc.…”

Section: Introductionmentioning

confidence: 99%

A new efficient implicit four-step method with vanished phase-lag and some of its derivatives for the numerical solution of the radial Schr¨odinger equation

Shokri¹,

Tahmourasi²

2017

J. of Mod. Meth. in Numer. Math.

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A new four-step implicit linear sixth algebraic order method with vanished phase-lag and its first derivative is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schrödinger equation and related problems. In order to produce an efficient multistep method the phase-lag property and its derivatives are used. The new method is analyzed for accuracy and periodicity properties, the error constants and interval and region of periodicity are investigated and obtained. The methods are compared with existing methods and they are tested on five problems from the literature.

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A family of two-stage two-step methods for the numerical integration of the Schrödinger equation and related IVPs with oscillating solution

Cited by 65 publications

References 78 publications

Numerical multistep methods for the efficient solution of quantum mechanics and related problems

Numerical multistep methods for the efficient solution of quantum mechanics and related problems

Exponentially Fitted Finite Difference Schemes for Reaction-Diffusion Equations

A new efficient implicit four-step method with vanished phase-lag and some of its derivatives for the numerical solution of the radial Schr¨odinger equation

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