New hybrid two-step method with optimized phase and stability characteristics

被引：15

作者：

Kovalnogov, V. N. ^{[1
]}

Fedorov, R., V ^{[1
]}

Bondarenko, A. A. ^{[2
]}

Simos, T. E. ^{[3
,4
,5
,6
,7
]}

机构：

[1] Ulyanovsk State Tech Univ, Fac Power Engn, Grp Numer & Appl Math Urgent Problems Energy & Po, Severny Venets St 32, Ulyanovsk 432027, Russia

[2] Ulyanovsk Inst Civil Aviat, Mozhaiskogo Str 8-8, Ulyanovsk 432071, Russia

[3] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh, Saudi Arabia

[4] Ural Fed Univ, Grp Modern Computat Methods, 19 Mira St, Ekaterinburg 620002, Russia

[5] TEI Sterea Hellas, Dept Automat Engn, 34400 Psachna Campus, Psachna, Greece

[6] Democritus Univ Thrace, Dept Civil Engn, Sect Math, Xanthi, Greece

[7] 10 Konitsis St, Athens 17564, Greece

来源：

JOURNAL OF MATHEMATICAL CHEMISTRY | 2018年 / 56卷 / 08期

基金：

俄罗斯基础研究基金会;

关键词：

Phase-lag; Derivative of the phase-lag; Initial value problems; Oscillating solution; Symmetric; Hybrid; Multistep; Schrodinger equation; INITIAL-VALUE-PROBLEMS; RADIAL SCHRODINGER-EQUATION; NUMEROV-TYPE METHODS; PREDICTOR-CORRECTOR METHOD; FINITE-DIFFERENCE PAIR; EXPLICIT 4-STEP METHOD; P-STABLE METHOD; TRIGONOMETRICALLY-FITTED FORMULAS; KUTTA-NYSTROM METHODS; NUMERICAL-SOLUTION;

D O I：

10.1007/s10910-018-0894-5

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

In this paper and for the first time in the literature, we develop a newRungeKutta type symmetric two-step finite difference pairwith the following characteristics: -the new algorithm is of symmetric type, -the new algorithm is of two-step, -the new algorithm is of five-stages, -the new algorithm is of twelfth-algebraic order, -the new algorithm is based on the following approximations: 1. the first layer on the point xn-1, 2. the second layer on the point xn-1, 3. the third layer on the point xn-1, 4. the fourth layer on the point xn and finally, 5. the fifth (final) layer on the point xn+ 1, -the new algorithm has vanished the phase-lag and its first, second, third and fourth derivatives, -the new algorithm has improved stability characteristics for the general problems, -the new algorithm is of P-stable type since it has an interval of periodicity equal to (0,8). For the new developed algorithm we present a detailed numerical analysis (local truncation error and stability analysis). The effectiveness of the new developed algorithm is evaluated with the approximate solution of coupled differential equations arising from the Schrodinger type.

引用

页码：2302 / 2340

页数：39