Exponential-fitting methods for the numerical solution of the schrodinger equation

Raptis, A. D.; Allison, A. C.

doi:10.1016/0010-4655(78)90047-4

Cited by 313 publications

(77 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Both the above mentioned methods are more efficient than the exponentially-fitted method of Raptis and Allison [42], which is indicated as Method RA.…”

Section: Discussionmentioning

confidence: 99%

“…Finally, the Method QT10 is more efficient than the hybrid sixth algebraic order method developed by Chawla and Rao with minimal phase-lag [44], which is indicated as Method MCR6 for large CPU time and less efficient than the Method MCR6 for small CPU time. 3.The twelfth algebraic order multistep method developed by Quinlan and Tremaine [41], which is indicated as Method QT12 is more efficient than the tenth order multistep method developed by Quinlan and Tremaine [41], which is indicated as Method QT10 4.The Phase-Fitted Method (Case 1) developed in [1], which is indicated as Method NMPF1 is more efficient than the classical form of the fourth algebraic order four-step method developed in Section 3, which is indicated as Method NMCL, the exponentially-fitted method of Raptis and Allison [42] and the Phase-Fitted Method (Case 2) developed in [1], which is indicated as Method NMPF2 5.The New Obtained Method developed in Section 3 (Case 2), which is indicated as Method NMC2 is more efficient than the classical form of the fourth algebraic order four-step method developed in Section 3, which is indicated as Method NMCL, the exponentially-fitted method of Raptis and Allison [42] and the Phase-Fitted Method (Case 2) developed in [1], which is indicated as Method NMPF2 and the Phase-Fitted Method (Case 1) developed in [1], which is indicated as Method NMPF1 6.The New Obtained Method developed in Section 3 (Case 2), which is indicated as Method NMC1 is the most efficient one.…”

Section: The Tenth Algebraic Order Multistep Methods Developedmentioning

confidence: 97%

“…-The fourth algebraic order method of Chawla and Rao with minimal phase-lag [43], which is indicated as Method MCR4 -The exponentially-fitted method of Raptis and Allison [42], which is indicated as Method RA -The hybrid sixth algebraic order method developed by Chawla and Rao with minimal phase-lag [44], which is indicated as Method MCR6 -The classical form of the fourth algebraic order fourstep method developed in Section 3, which is indicated as Method NMCL 3 .…”

Section: Radial Schrödinger Equation -The Resonance Problemmentioning

confidence: 99%

See 2 more Smart Citations

On the Explicit Four-Step Methods with Vanished Phase-Lag and its First Derivative

Simos¹

2014

Appl. Math. Inf. Sci.

121

View full text Add to dashboard Cite

Abstract:In the present paper, we will investigate a family of explicit four-step methods first introduced by Anastassi and Simos [1] for the case of vanishing of phase-lag and its first derivative. These methods are efficient for the numerical solution of the Schrödinger equation and related initial-value or boundary-value problems with periodic and/or oscillating solutions. As we mentioned before the main scope of this paper is the study of the elimination of the phase-lag and its first derivative of the family of the methods to be investigated. A comparative error and stability analysis will be presented for the studied family of four-step explicit methods. The new obtained methods will finally be tested on the resonance problem of the Schrödinger equation in order to examine their efficiency.

show abstract

“…Both the above mentioned methods are more efficient than the exponentially-fitted method of Raptis and Allison [42], which is indicated as Method RA.…”

Section: Discussionmentioning

confidence: 99%

Section: The Tenth Algebraic Order Multistep Methods Developedmentioning

confidence: 97%

Section: Radial Schrödinger Equation -The Resonance Problemmentioning

confidence: 99%

See 1 more Smart Citation

On the Explicit Four-Step Methods with Vanished Phase-Lag and its First Derivative

Simos¹

2014

Appl. Math. Inf. Sci.

121

View full text Add to dashboard Cite

show abstract

“…We mention here that in the literature the last decades there are several variable step procedures for the approximation of the solution for systems of Schrödinger type equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Error Estimationmentioning

confidence: 99%

A New Algorithm for the Approximation of the Schrödinger Equation

Lin

Simos

2016

Open Physics

View full text Add to dashboard Cite

Abstract:In this paper a four stages twelfth algebraic order symmetric two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives is developed for the first time in the literature. For the new proposed method: (1) we will study the phase-lag analysis, (2) we will present the development of the new method, (3) the local truncation error (LTE) analysis will be studied. The analysis is based on a test problem which is the radial time independent Schrödinger equation, (4) the stability and the interval of periodicity analysis will be presented, (5) stepsize control technique will also be presented, (6) the examination of the accuracy and computational cost of the proposed algorithm which is based on the approximation of the Schrödinger equation.

show abstract

“…• The Exponentially-fitted four-step method developed by Raptis [35] which is indicated as Method I.…”

Section: The Methodsmentioning

confidence: 99%

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

Shokri

Tahmourasi²

2017

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

View full text Add to dashboard Cite

A new four-step implicit linear eight algebraic order method with vanished phase-lag and its first, second and third derivatives 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. An error analysis and a stability analysis is also investigated and a comparison with other methods is also studied. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.

show abstract

Exponential-fitting methods for the numerical solution of the schrodinger equation

Cited by 313 publications

References 9 publications

On the Explicit Four-Step Methods with Vanished Phase-Lag and its First Derivative

On the Explicit Four-Step Methods with Vanished Phase-Lag and its First Derivative

A New Algorithm for the Approximation of the Schrödinger Equation

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

Contact Info

Product

Resources

About