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      Least Square Homotopy Perturbation Method for Ordinary Differential Equations

      1 , 1
      Journal of Mathematics
      Hindawi Limited

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          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.

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          Most cited references32

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          Homotopy perturbation technique

          Ji-Huan He (1999)
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            Homotopy perturbation method for Fangzhu oscillator

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              Homotopy Perturbation Method for the Fractal Toda Oscillator

              The fractal Toda oscillator with an exponentially nonlinear term is extremely difficult to solve; Elias-Zuniga et al. (2020) suggested the equivalent power-form method. In this paper, first, the fractal variational theory is used to show the basic property of the fractal oscillator, and a new form of the Toda oscillator is obtained free of the exponential nonlinear term, which is similar to the form of the Jerk oscillator. The homotopy perturbation method is used to solve the fractal Toda oscillator, and the analytical solution is examined using the numerical solution which shows excellent agreement. Furthermore, the effect of the order of the fractal derivative on the vibration property is elucidated graphically.
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                Author and article information

                Contributors
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                Journal
                Journal of Mathematics
                Journal of Mathematics
                Hindawi Limited
                2314-4785
                2314-4629
                October 5 2021
                October 5 2021
                : 2021
                : 1-16
                Affiliations
                [1 ]National University of Computer and Emerging Sciences FAST, Lahore, Pakistan
                Article
                10.1155/2021/7059194
                b20d23ba-67c5-412e-8146-5c83f83be1aa
                © 2021

                https://creativecommons.org/licenses/by/4.0/

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