Solution of delay differential equations via a homotopy perturbation method

Authors:
Fatemeh Shakeri;Mehdi Dehghan
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

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Abstract

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.