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

页码：1480 / 1504

页数：25

共 144 条

[21] HIGH-ACCURACY P-STABLE METHODS FOR Y'' = F(T,Y) [J].

CHAWLA, MM ;

RAO, PS .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1985, 5 (02) :215-220

[22] FAMILIES OF 2-STEP 4TH-ORDER P-STABLE METHODS FOR 2ND-ORDER DIFFERENTIAL-EQUATIONS [J].

CHAWLA, MM ;

NETA, B .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1986, 15 (02) :213-223

[23] A NEW CLASS OF EXPLICIT 2-STEP 4TH ORDER METHODS FOR Y'' = F(T, Y) WITH EXTENDED INTERVALS OF PERIODICITY [J].

CHAWLA, MM .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1986, 14 (03) :467-470

[24] INTERVALS OF PERIODICITY AND ABSOLUTE STABILITY OF EXPLICIT NYSTROM METHODS FOR Y''=F(X,Y) [J].

CHAWLA, MM ;

SHARMA, SR .

BIT, 1981, 21 (04) :455-464

[25] Singly-implicit stabilized extended one-step methods for second-order initial-value problems with oscillating solutions [J].

Chawla, MM ;

Al-Zanaidi, MA ;

Al-Ghonaim, SS .

MATHEMATICAL AND COMPUTER MODELLING, 1999, 29 (02) :63-72

[26] A NOUMEROV-TYPE METHOD WITH MINIMAL PHASE-LAG FOR THE INTEGRATION OF 2ND ORDER PERIODIC INITIAL-VALUE PROBLEMS [J].

CHAWLA, MM ;

RAO, PS .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1984, 11 (03) :277-281

[27] AN EXPLICIT 6TH-ORDER METHOD WITH PHASE-LAG OF ORDER 8 FOR Y''=F(T, Y) [J].

CHAWLA, MM ;

RAO, PS .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1987, 17 (03) :365-368

[28] Highly-accurate ground state energies of the He atom and the He-like ions by Hartree SCF calculation with Obrechkoff method [J].

Chen, Jiaqi ;

Wang, Zhongcheng ;

Shao, Hezhu ;

Hao, Hailing .

COMPUTER PHYSICS COMMUNICATIONS, 2008, 179 (07) :486-491

[29] The arbitrary order implicit multistep schemes of exponential fitting and their applications [J].

Chen, T ;

Yan, HQ ;

Hao, Z ;

Chen, ZQ ;

Ming, L ;

Zhang, GM .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 173 (01) :155-168

[30] Truncation errors in exponential fitting for oscillatory problems [J].

Coleman, J. P. ;

Ixaru, L. Gr. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (04) :1441-1465

← 1 2 3 4 5 6 7 8 9 10 →