Shakeri, Fatemeh; Dehghan, Mehdi Solution of delay differential equations via a homotopy perturbation method. (English) Zbl 1145.34353 Math. Comput. Modelling 48, No. 3-4, 486-498 (2008). Summary: 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. Cited in 139 Documents MSC: 34K06 Linear functional-differential equations 65L99 Numerical methods for ordinary differential equations 92D99 Genetics and population dynamics Keywords:delay differential equations; homotopy perturbation method; applications in mathematical biology and engineering PDFBibTeX XMLCite \textit{F. Shakeri} and \textit{M. Dehghan}, Math. Comput. Modelling 48, No. 3--4, 486--498 (2008; Zbl 1145.34353) Full Text: DOI References: [1] Kuang, Y., Delay Differential Equations with Applications in Population Dynamics (1993), Academic press, Inc.: Academic press, Inc. New York · Zbl 0777.34002 [2] Dugard, L.; Verriest, E. I., (Stability and Control of Time-delay Systems. Stability and Control of Time-delay Systems, Lecture Notes in Control and Information Sciences, vol. 228 (1997), Springer) [3] He, J. H., Homotopy perturbation technique, Computational Methods in Applied Mechanics and Engineering, 178, 257-262 (1999) · Zbl 0956.70017 [4] He, J. 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