Neural Network Solution of Single-Delay Differential Equations

被引：47

作者：

Fang, Jie ^{[1
]}

Liu, Chenglian ^{[2
]}

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

Famelis, I. Th. ^{[8
]}

机构：

[1] Fujian Normal Univ, Sch Elect & Informat Engn, Fuqing Branch, Fuqing 350300, Peoples R China

[2] Neusoft Inst Guangdong, Dept Comp Sci & Technol, Foshan 528228, Peoples R China

[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[4] South Ural State Univ, 76 Lenin Ave, Chelyabinsk 454080, Russia

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

[6] Neijiang Normal Univ, Data Recovery Key Lab Sichuan Prov, Dongtong Rd 705, Neijiang 641100, Peoples R China

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

[8] Univ West Attica, Dept Elect & Elect Engn, MicroSENSES Lab, Athens, Greece

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2020年 / 17卷 / 01期

关键词：

Neural networks; delay differential equations; VANISHED PHASE-LAG; RUNGE-KUTTA PAIRS; INITIAL-VALUE PROBLEMS; NUMEROV-TYPE METHODS; P-STABLE METHOD; NUMERICAL-SOLUTION; HIGH-ORDER; FITTED MODIFICATIONS; SOLVING ORDINARY; NYSTROM METHODS;

D O I：

10.1007/s00009-019-1452-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Following the ideas of Lagaris et al. (IEEE Trans Neural Netw 9(5):987-1000, 1998), we use Neural Networks to solve approximatively first-order single-delay differential equations and systems. We apply the proposed novel methodology to various problems with constant delay terms and the resulted continuous solutions prove to be very efficient. This is the case not only for nonstiff problems but for equations with stiffness too.

引用

页数：15

共 51 条

[1] A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrodinger equation [J].

Alolyan, Ibraheem ;

Simos, T. E. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (10) :3756-3774

[2]

[Anonymous], 2010, MATLAB, Version 7.10.0

[3]

[Anonymous], 1977, APPLMATH SCI

[4]

[Anonymous], 2016, Numerical Methods for Ordinary Differential Equations

[5]

ARNDT H, 1984, NUMER MATH, V43, P343, DOI 10.1007/BF01390178

[6]

Arndt H., 1983, DIFFERENTIAL DIFFERE, P9

[7]

Arndt H., 1985, INT S U MANNH SPR, P41

[8]

Baker C.T.H., 1999, NUM ANAL REP, V343

[9]

Baker C.T.H., 1994, NUM ANAL REPORT, V248

[10] Modelling and analysis of time-lags in some basic patterns of cell proliferation [J].

Baker, CTH ;

Bocharov, GA ;

Paul, CAH ;

Rihan, FA .

JOURNAL OF MATHEMATICAL BIOLOGY, 1998, 37 (04) :341-371

← 1 2 3 4 5 6 →