A phase-fitting, first and second derivatives phase-fitting singularly P-stable economical two-step method for problems in chemistry

被引：14
作者：
Sun, Bin [1 ,2 ]
Lin, Chia-Liang [2 ,3 ]
Simos, T. E. [4 ,5 ,6 ]
机构：
[1] Jingdezhen Ceram Univ, Jingdezhen 333002, Jiangxi, Peoples R China
[2] Huzhou Univ, Huzhou 313000, Zhejiang, Peoples R China
[3] Natl & Kapodistrian Univ Athens, Gen Dept, Euripus Campus, Chalkis 34400, Greece
[4] China Med Univ, Taichung, Taiwan
[5] Neijiang Normal Univ, Data Recovery Key Lab Sichuan Prov, Dongtong Rd 705, Neijiang 641100, Peoples R China
[6] Democritus Univ Thrace, Dept Civil Engn, Sect Math, Xanthi, Greece
来源：
JOURNAL OF MATHEMATICAL CHEMISTRY | 2022年 / 60卷 / 08期
关键词：
Phase-lag; Derivative of the phase-lag; Initial value problems; Oscillating solution; Symmetric; Hybrid; Multistep; Schrodinger equation; RUNGE-KUTTA METHODS; INITIAL-VALUE PROBLEMS; ONE-STEP METHODS; EXPONENTIAL-FITTED METHODS; NOUMEROV-TYPE METHOD; NUMEROV-TYPE METHOD; HIGH-ORDER METHOD; NUMERICAL-SOLUTION; NYSTROM METHODS; OBRECHKOFF METHODS;
D O I：
10.1007/s10910-022-01361-8
中图分类号：
O6 [化学];
学科分类号：
0703 ;
摘要：
A phase-fitting, first and second derivatives phase-fitting method is produced. The new algorithm is singularly P-Stable and belongs to the economic algorithms. The new method is symbolized as PF2DPFN2SPS. It can be used to any problem with periodical and/or oscillating solutions. We chosen to be applied to a well known problem of Quantum Chemistry. The new scheme is an economic one because 5 function evaluations per step are used in order an algebraic order (AOR) of 12 to be achieved.
引用
收藏
页码：1480 / 1504
页数：25
相关论文
共 144 条
[81]  
LAMBERT JD, 1976, J I MATH APPL, V18, P189
[82]  
Lambert JD, 1991, Numerical Methods for Ordinary Differential Systems: The Initial Value Problem
[83]  
Leach A. R., 2001, Molecular Modelling: Principles and Applications, V2nd ed.
[84]   A complete in phase FiniteDiffrnc algorithm for DiffrntEqutins in chemistry [J].
Lin, Chia-Liang ;
Simos, T. E. .
JOURNAL OF MATHEMATICAL CHEMISTRY, 2020, 58 (06) :1091-1132
[85]   CHEBYSHEVIAN MULTISTEP METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS [J].
LYCHE, T .
NUMERISCHE MATHEMATIK, 1972, 19 (01) :65-&
[86]   An efficient and computational effective method for second order problems [J].
Ma, Jing ;
Simos, T. E. .
JOURNAL OF MATHEMATICAL CHEMISTRY, 2017, 55 (08) :1649-1668
[87]   Exponential fitted Gauss, Radau and Lobatto methods of low order [J].
Martin-Vaquero, J. ;
Vigo-Aguiar, J. .
NUMERICAL ALGORITHMS, 2008, 48 (04) :327-346
[88]   Adapted BDF algorithms:: Higher-order methods and their stability [J].
Martin-Vaquero, J. ;
Vigo-Aguiar, J. .
JOURNAL OF SCIENTIFIC COMPUTING, 2007, 32 (02) :287-313
[89]  
Medvedev M.A., J MATH CHEM
[90]   A three-stages multistep teeming in phase algorithm for computational problems in chemistry [J].
Medvedev, Maxim A. ;
Simos, T. E. .
JOURNAL OF MATHEMATICAL CHEMISTRY, 2019, 57 (06) :1598-1617
45678910111213