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Least Square Homotopy Perturbation Method for Ordinary Differential Equations

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  • Mubashir Qayyum
  • Imbsat Oscar
  • Gaetano Luciano

Abstract

In this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). The proposed scheme is tested against various linear and nonlinear BVPs (second to seventh order DEs). Validity of the obtained solutions is confirmed by finding absolute errors. To analyze the efficiency of the proposed scheme, tested problems have also been solved through HPM and results are compared with LSHPM. Furthermore, obtained results are also compared with other numerical schemes available in literature. Analysis reveals that LSHPM is a consistent and effective scheme which can be used for more complex BVPs in science and engineering.

Suggested Citation

  • Mubashir Qayyum & Imbsat Oscar & Gaetano Luciano, 2021. "Least Square Homotopy Perturbation Method for Ordinary Differential Equations," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, October.
    • Handle: RePEc:hin:jjmath:7059194
    DOI: 10.1155/2021/7059194
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    Cited by:

    1. Mădălina Sofia Paşca & Olivia Bundău & Adina Juratoni & Bogdan Căruntu, 2022. "The Least Squares Homotopy Perturbation Method for Systems of Differential Equations with Application to a Blood Flow Model," Mathematics, MDPI, vol. 10(4), pages 1-14, February.

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