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

[31] A new high order two-step method with vanished phase-lag and its derivatives for the numerical integration of the Schrodinger equation
Alolyan, Ibraheem
Simos, T. E.
JOURNAL OF MATHEMATICAL CHEMISTRY, 2012, 50 (09) : 2351 - 2373
[32] On the Explicit Four-Step Methods with Vanished Phase-Lag and its First Derivative
Simos, T. E.
APPLIED MATHEMATICS & INFORMATION SCIENCES, 2014, 8 (02): : 447 - 458
[33] A family of Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the Schrodinger equation and related problems
Anastassi, Z. A.
Vlachos, D. S.
Simos, T. E.
JOURNAL OF MATHEMATICAL CHEMISTRY, 2009, 46 (04) : 1158 - 1171
[34] Four-Stages Twelfth Algebraic Order Two-Step Method with Vanished Phase-Lag and its First and Second Derivatives for the Numerical Solution of the Schrodinger Equation
Lei, Tao
Simos, Theodore E.
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2016, 76 (02) : 475 - 510
[35] A new hybrid two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrodinger equation and related problems
Alolyan, Ibraheem
Simos, T. E.
JOURNAL OF MATHEMATICAL CHEMISTRY, 2012, 50 (07) : 1861 - 1881
[36] A modified Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrodinger equation and related problems
Simos, TE
Vigo-Aguiar, J
COMPUTERS & CHEMISTRY, 2001, 25 (03): : 275 - 281
[37] Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation
Ibraheem Alolyan
T. E. Simos
Journal of Mathematical Chemistry, 2010, 48 : 1092 - 1143
[38] Construction of an Optimized Explicit Runge-Kutta Method with Increased Phase-Lag Order for the Numerical Solution of the Schrodinger Equation
Kosti, A. A.
Anastassi, Z. A.
Simos, T. E.
INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2009 (ICCMSE 2009), 2012, 1504 : 1182 - 1184
[39] On Eight-Step Methods with Vanished Phase-Lag and Its Derivatives for the Numerical Solution of the Schrodinger Equation
Alolyan, Ibraheem
Simos, Theodore E.
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2011, 66 (02) : 473 - 546
[40] A Runge-Kutta Method with Zero Phase-Lag and Derivatives for the Numerical Solution of Orbital Problems
Papadopoulos, D. F.
Simos, T. E.
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B, 2012, 1479 : 1399 - 1402

← 1 2 3 4 5 →