A Linear Four-Step Method with Vanished Phase-Lag and its First and Second Derivatives for the Numerical Solution of Periodic Initial and/or Boundary Value Problems

被引：0
作者：
Simos, T. E. [1 ]
机构：
[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia
来源：
INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2014 (ICCMSE 2014) | 2014年 / 1618卷
关键词：
Numerical solution; Schrodinger equation; linear multistep methods; interval of periodicity; P-stability; phase-lag; phase-fitted; derivatives of the phase-lag; PREDICTOR-CORRECTOR METHOD; KUTTA-NYSTROM METHODS; SCHRODINGER-EQUATION; OSCILLATING SOLUTIONS; EFFICIENT INTEGRATION; ORBITAL PROBLEMS; ORDER; IVPS; FAMILY; FORMULAS;
D O I：
10.1063/1.4897910
中图分类号：
O59 [应用物理学];
学科分类号：
摘要：
A linear explicit four-step method with vanished phase-lag and its first and second derivatives for the numerical solution of second order initial or boundary-value problems with periodical and/or oscillating behavior of the solution is investigated in this paper. We base the construction of the new proposed method on the vanishing of the phase-lag and its first and second derivatives. A comparative local truncation error analysis with other similar methods of the literature is investigated. The stability analysis for the new obtained methos is also presented. The effectiveness of the new developed method is shown with an application of this method to the resonance problem of the one dimensional time independent Schrodinger equation.
引用
收藏
页码：1031 / 1035
页数：5
相关论文
共 28 条
[11]   An exponentially-fitted and trigonometrically-fitted method for the numerical solution of periodic initial-value problems [J].
Konguetsof, A ;
Simos, TE .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2003, 45 (1-3) :547-554
[12]   Construction of an optimized explicit Runge-Kutta-Nystrom method for the numerical solution of oscillatory initial value problems [J].
Kosti, A. A. ;
Anastassi, Z. A. ;
Simos, T. E. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (11) :3381-3390
[13]  
Lambert J.D., 1991, NUMERICAL METHODS OR, P104
[14]   Exponentially Fitted Symplectic Runge-Kutta-Nystrom methods [J].
Monovasilis, Th. ;
Kalogiratou, Z. ;
Simos, T. E. .
APPLIED MATHEMATICS & INFORMATION SCIENCES, 2013, 7 (01) :81-85
[15]   A family of trigonometrically fitted partitioned Runge-Kutta symplectic methods [J].
Monovasilis, Th. ;
Kalogiratou, Z. ;
Simos, T. E. .
APPLIED MATHEMATICS AND COMPUTATION, 2009, 209 (01) :91-96
[16]   A New Optimized Symmetric Embedded Predictor-Corrector Method (EPCM) for Initial-Value Problems with Oscillatory Solutions [J].
Panopoulos, G. A. ;
Simos, T. E. .
APPLIED MATHEMATICS & INFORMATION SCIENCES, 2014, 8 (02) :703-713
[17]   An Optimized Symmetric 8-Step Semi-Embedded Predictor-Corrector Method for IVPs with Oscillating Solutions [J].
Panopoulos, G. A. ;
Simos, T. E. .
APPLIED MATHEMATICS & INFORMATION SCIENCES, 2013, 7 (01) :73-80
[18]   The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge-Kutta-Nystrom Method [J].
Papadopoulos, D. F. ;
Simos, T. E. .
ABSTRACT AND APPLIED ANALYSIS, 2013,
[19]   A Modified Runge-Kutta-Nystrom Method by using Phase Lag Properties for the Numerical Solution of Orbital Problems [J].
Papadopoulos, Dimitris F. ;
Simos, T. E. .
APPLIED MATHEMATICS & INFORMATION SCIENCES, 2013, 7 (02) :433-437
[20]   A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions [J].
Psihoyios, G ;
Simos, TE .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 175 (01) :137-147
123