A Runge-Kutta type four-step method with vanished phase-lag and its first and second derivatives for each level for the numerical integration of the Schrodinger equation

被引：82

作者：

Alolyan, Ibraheem ^{[1
]}

Simos, T. E. ^{[1
,2
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

[2] Univ Peloponnese, Fac Econ Management & Informat, Dept Informat & Telecommun, Sci Computat Lab, Tripolis 22100, Greece

来源：

JOURNAL OF MATHEMATICAL CHEMISTRY | 2014年 / 52卷 / 03期

关键词：

Schrodinger equation; Multistep methods; Hybrid methods; Runge-Kutta type methods; Interval of periodicity; P-stability; Phase-lag; Phase-fitted; Derivatives of the phase-lag; TRIGONOMETRICALLY-FITTED FORMULAS; PREDICTOR-CORRECTOR METHOD; INITIAL-VALUE PROBLEMS; SYMMETRIC MULTISTEP METHODS; HYBRID EXPLICIT METHODS; LONG-TIME INTEGRATION; NUMEROV-TYPE METHOD; HIGH-ORDER; SYMPLECTIC METHODS; INTERNATIONAL-CONFERENCE;

D O I：

10.1007/s10910-013-0301-1

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

The investigation of the impact of the vanishing of the phase-lag and its first and second derivatives on the efficiency of a four-step Runge-Kutta type method of sixth algebraic order is presented in this paper. Based on the above mentioned investigation, a Runge-Kutta type of two level four-step method of sixth algebraic order is produced. The error and the stability of the new obtained method are also studied in the present paper. The obtained new method is applied to the resonance problem of the Schrodinger equation the efficiency of the method to be examined.

引用

页码：917 / 947

页数：31

共 50 条

[41] An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrodinger equation and related problems
Kosti, A. A.
Anastassi, Z. A.
Simos, T. E.
JOURNAL OF MATHEMATICAL CHEMISTRY, 2010, 47 (01) : 315 - 330
[42] A high algebraic order multistage explicit four-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives for the numerical solution of the Schrödinger equation
Ibraheem Alolyan
T. E. Simos
Journal of Mathematical Chemistry, 2015, 53 : 1915 - 1942
[43] High order four-step hybrid method with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation
Ibraheem Alolyan
T. E. Simos
Journal of Mathematical Chemistry, 2013, 51 : 532 - 555
[44] A New Four-Stages High Algebraic Order Two-Step Method with Vanished Phase-Lag and its First, Second and Third Derivatives for the Numerical Solution of the Schrodinger Equation
Cheng, Xin
Simos, Theodore E.
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2017, 77 (02) : 527 - 568
[45] A New Four-Stages Twelfth Algebraic Order Two-Step Method with Vanished Phase-Lag and Its First, Second, Third and Fourth Derivatives for the Numerical Solution of the Schrodinger Equation
Xi, Xiaopeng
Simos, Theodore E.
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2017, 77 (02) : 333 - 392
[46] A new high algebraic order four stages symmetric two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrodinger equation and related problems
Xi, Xiaopeng
Simos, T. E.
JOURNAL OF MATHEMATICAL CHEMISTRY, 2016, 54 (07) : 1417 - 1439
[47] A new two stage symmetric two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrodinger equation
Zhou, Zhou
Simos, T. E.
JOURNAL OF MATHEMATICAL CHEMISTRY, 2016, 54 (02) : 442 - 465
[48] New two stages high order symmetric six-step method with vanished phase-lag and its first, second and third derivatives for the numerical solution of the Schrodinger equation
Alolyan, Ibraheem
Simos, T. E.
JOURNAL OF MATHEMATICAL CHEMISTRY, 2017, 55 (02) : 503 - 531
[49] High order computationally economical six-step method with vanished phase-lag and its derivatives for the numerical solution of the Schrodinger equation
Berg, Dmitriy B.
Simos, T. E.
JOURNAL OF MATHEMATICAL CHEMISTRY, 2017, 55 (04) : 987 - 1013
[50] A new four stages symmetric two-step method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation
Minjian Liang
T. E. Simos
Journal of Mathematical Chemistry, 2016, 54 : 1187 - 1211

← 1 2 3 4 5 →