A differential transformation approach for solving functional differential equations with multiple delays

被引：15

作者：

Rebenda, Josef ^{[1
]}

Smarda, Zdenek ^{[1
]}

机构：

[1] Brno Univ Technol, CEITEC BUT, Purkynova 123, Brno 61200, Czech Republic

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2017年 / 48卷

关键词：

Delayed differential equation; Neutral differential equation; Differential transformation method; Method of steps; INTEGRODIFFERENTIAL EQUATIONS; BIOLOGY; MODEL;

D O I：

10.1016/j.cnsns.2016.12.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper an efficient semi-analytical approach based on the method of steps and the differential transformation is proposed for numerical approximation of solutions of functional differential models of delayed and neutral type on a finite interval of arbitrary length, including models with several constant delays. Algorithms for both commensurate and non-commensurate delays are described, applications are shown in examples. Validity and efficiency of the presented algorithms is compared with the variational iteration method, the Adomian decomposition method and the polynomial least squares method numerically. Matlab package DDE23 is used to produce reference numerical values.

引用

页码：246 / 257

页数：12

共 27 条

[1] Solution of Delay Differential Equation by Means of Homotopy Analysis Method
Alomari, A. K.
Noorani, M. S. M.
Nazar, R.
[J]. ACTA APPLICANDAE MATHEMATICAE, 2009, 108 (02) : 395 - 412
[2] [Anonymous], 2003, Numerical Methods for Delay Differential Equations
[3] Solution of differential-difference equations by using differential transform method
Arikoglu, Aytac
Ozkol, Ibrahim
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 181 (01) : 153 - 162
[4] Numerical solution of delay integro-differential equations by using Taylor collocation method
Bellour, Azzeddine
Bousselsal, Mahmoud
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2014, 37 (10) : 1491 - 1506
[5] Solving delay differential systems with history functions by the Adomian decomposition method
Blanco-Cocom, Luis
Estrella, Angel G.
Avila-Vales, Eric
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (10) : 5994 - 6011
[6] Caruntu B, 2014, SCI WORLD J, V6
[7] The variational iteration method for solving a neutral functional-differential equation with proportional delays
Chen, Xumei
Wang, Linjun
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (08) : 2696 - 2702
[8] Solution of a nonlinear time-delay model in biology via semi-analytical approaches
Dehghan, Mehdi
Salehi, Rezvan
[J]. COMPUTER PHYSICS COMMUNICATIONS, 2010, 181 (07) : 1255 - 1265
[9] The Adomian decomposition method for solving delay differential equation
Evans, DJ
Raslan, KR
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2005, 82 (01) : 49 - 54
[10] Gyori I., 1991, Oscillation theory of delay differential equations with applications

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