Homotopy Perturbation Method of Delay Differential Equation Using He’s Polynomial with Laplace Transform
- 9 Downloads
In this article, we report a combined concept of linearties and nonlinearties of homotopy perturbation method using Laplace transform with He’s polynomials for solving complex delay differential equations which have a versatile application in signal processing, digital image processing, physics and applied sciences. Some examples are given to illustrate the ability and reliability of the proposed method, and the results are compared with VIM and exact solution after taking sum of first four iterations of approximate solution. Convergence analysis is discussed after implementing Banach fixed point theorem.
KeywordsDelay differential equations Homotopy perturbation method He’s polynomials Laplace transform Initial value problem Convergence analysis
Mathematics Subject Classification3397 10970
The first author acknowledges the financial support provided by the Madhya Pradesh Council of Science and Technology (MPCST),under research Grant No. 1013/CST/R&D/Phy&EnggSc/2015; Bhopal, Madhya Pradesh, India. The authors also extended their appreciations to anonymous reviewers for their valuable suggestions to revise this paper.
- 10.Sara Barati, Karim Ivaz (2012) Variational iteration method for solving systems of linear delay differential equations. Int Sch Sci Res Innov 6:964–967Google Scholar
- 20.Tripathi R, Mishra HK (2016) Homotopy perturbation method with Laplace transform (LT-HPM) for solving Lane–Emden type differential equations (LETDEs). Springer Plus 5(1859):1–21Google Scholar
- 21.Murray Spiegel R (1988) Teoríay Problemas de Transformadas de Laplace Primeraedición. Serie de compendious Schaum. McGraw-Hill, Mexico City, pp 1–261Google Scholar
- 24.Ogunfiditimi FO (2015) Numerical solution of delay differential equations using the Adomian decomposition method. Int J Eng Sci 4(5):8–23Google Scholar
- 26.Bellen A, Zennro M (2003) Numerical methods for delay differential equations. Clarendon Press, Oxford, pp 1–416Google Scholar
- 28.Mishra HK (2014) He–Laplace method for the solution of two-point boundary value. Probl Am J Math Anal 2(3):45–49Google Scholar