# A new two-step hybrid method for the numerical solution of the Schrödinger equation

@article{Konguetsof2010ANT, title={A new two-step hybrid method for the numerical solution of the Schr{\"o}dinger equation}, author={Avrilia Konguetsof}, journal={Journal of Mathematical Chemistry}, year={2010}, volume={47}, pages={871-890} }

With this paper, a new algorithm is developed for the numerical solution of the one-dimensional Schrödinger equation. The new method uses the minimum order of the phase-lag and its derivatives. Error analysis and the numerical results illustrate the efficiency of the new algorithm.

## 96 Citations

### A new high order two-step method with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation

- MathematicsJournal of Mathematical Chemistry
- 2012

In this paper we develop a new hybrid method of high order with phase-lag and its first, second and third derivatives equal to zero. For the produced method we study its error and stability. We apply…

### Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation

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In this paper we present a new method for the numerical solution of the time-independent Schrödinger equation for one spatial dimension and related problems. A technique, based on the phase-lag and…

### A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equation

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- 2011

In this paper we introduce a new explicit hybrid Numerov-type method. This method is of fourth algebraic order and has phase-lag and its first two derivatives equal to zero. We present a stability…

### High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation

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- 2010

In the present paper we develop a high algebraic order multistep method. The characteristic property of the new proposed method is the requirement of vanishing the phase-lag and its derivatives. The…

### Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation

- Mathematics, PhysicsJournal of Mathematical Chemistry
- 2016

A new family of exponentially fitted P-stable one-step linear methods involving several derivatives for the numerical integration of the Schrödinger equation are obtained. Numerical results are…

### A new hybrid two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrödinger equation and related problems

- MathematicsJournal of Mathematical Chemistry
- 2012

The maximization of the efficiency of a hybrid two-step method for the numerical solution of the radial Schrödinger equation and related problems with periodic or oscillating solutions via the…

### A family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation

- Mathematics
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A family of high algebraic order ten-step methods is obtained in this paper. The new developed methods have vanished phase-lag (the first one) and phase-lag and its first derivative (the second one).…

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- Mathematics
- 2011

A family of hybrid methods with algebraic order eight is proposed, with phase-lag and its first four derivatives eliminated. We investigate the behavior of the new algorithm and the property of the…

### High order four-step hybrid method with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation

- MathematicsJournal of Mathematical Chemistry
- 2012

AbstractIn this paper, we develop a new four-step hybrid method of sixth algebraic order with vanished phase-lag and its first and second derivatives. For the obtained method we study:
– its error…

### A new four-step hybrid type method with vanished phase-lag and its first derivatives for each level for the approximate integration of the Schrödinger equation

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- 2013

In this paper we present a new methodology for the development of four-step hybrid type methods of sixth algebraic order with vanished phase-lag and its derivatives. The methodology is based on the…

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