Trigonometric fitted, eighth-order explicit Numerov-type methods

被引：62

作者：

Berg, Dmitry B. ^{[1
]}

Simos, T. E. ^{[2
,3
]}

Tsitouras, Ch. ^{[3
]}

机构：

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

[2] Neijiang Normal Univ, Coll Math & Informat Sci, Data Recovery Key Lab Sichuan Prov, Neijiang 641100, Peoples R China

[3] TEI Sterea Hellas, Dept Automat Engn, GR-34400 Psahna, Greece

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 05期

关键词：

hybrid Numerov methods; initial value problem; numerical solution; phase lag; variable coefficients; INITIAL-VALUE-PROBLEMS; VANISHED PHASE-LAG; KUTTA-NYSTROM METHODS; P-STABLE METHOD; PREDICTOR-CORRECTOR METHOD; 2ND-ORDER LINEAR IVPS; 2-STEP HYBRID METHODS; NOUMEROV-TYPE METHOD; SCHRODINGER-EQUATION; NUMERICAL-INTEGRATION;

D O I：

10.1002/mma.4711

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the integration of the special second-order initial value problem of the form y=f(x,y). A recently introduced family of 7 stages, eighth-order methods, sharing constant coefficients, is used as base. This family is properly modified to derive phase fitted and zero dissipative methods (ie, trigonometric fitted) that are best suited for integrating oscillatory problems. Numerical tests over a set of problems shows enhanced performance when the purely linear part of the problems is rather large in comparison with the rest of nonlinear parts. An appendix implementing a MATLAB listing with the coefficients of the new method is also given.

引用

页码：1845 / 1854

页数：10

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