Solution of delay differential equations via a homotopy perturbation method

Delay differential equations (denoted as DDE) have a wide range of application in science and engineering. They arise when the rate of change of a time-dependent process in its mathematical modeling is not only determined by its present state but also by a certain past state. Recent studies in such...

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Vydáno v:Mathematical and computer modelling Ročník 48; číslo 3; s. 486 - 498
Hlavní autoři: Shakeri, Fatemeh, Dehghan, Mehdi
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Elsevier Ltd 01.08.2008
Elsevier Science
Témata:
Applications in mathematical biology and engineering
Delay differential equations
Exact sciences and technology
Homotopy perturbation method
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
Delay differential equations
Homotopy perturbation method
Applications in mathematical biology and engineering
Differential equation
Numerical method
Delay equation
Perturbation method
Numerical analysis
Scientific computation
Applied mathematics
Homotopy
Mathematical model
Computer aided analysis
ISSN:0895-7177, 1872-9479
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Popis
Shrnutí:Delay differential equations (denoted as DDE) have a wide range of application in science and engineering. They arise when the rate of change of a time-dependent process in its mathematical modeling is not only determined by its present state but also by a certain past state. Recent studies in such diverse fields as biology, economy, control and electrodynamics have shown that DDEs play an important role in explaining many different phenomena. In particular they turn out to be fundamental when ODE-based models fail. In this research, the solution of a delay differential equation is presented by means of a homotopy perturbation method and then some numerical illustrations are given. These results reveal that the proposed method is very effective and simple to perform.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2007.09.016