Homotopy Perturbation Method of Delay Differential Equation Using He’s Polynomial with Laplace Transform

Abstract

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.

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Acknowledgements

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.

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Correspondence to Hradyesh Kumar Mishra.

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Mishra, H.K., Tripathi, R. Homotopy Perturbation Method of Delay Differential Equation Using He’s Polynomial with Laplace Transform. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 90, 289–298 (2020). https://doi.org/10.1007/s40010-018-0581-8

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Keywords

  • Delay differential equations
  • Homotopy perturbation method
  • He’s polynomials
  • Laplace transform
  • Initial value problem
  • Convergence analysis

Mathematics Subject Classification

  • 3397
  • 10970