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Application of Local Fractional Homotopy Perturbation Method in Physical Problems

Author

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  • Nabard Habibi
  • Zohre Nouri

Abstract

Nonlinear phenomena have important effects on applied mathematics, physics, and issues related to engineering. Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. The perturbation method is a wave equation solution using HPM compared with the Fourier series method, and both methods results are good agreement. The percentage of error of u(x, t) with α = 1 and 0.33, t =0.1 sec, between the present research and Yong‐Ju Yang study for x ≥ 0.6 is less than 10. Also, the % error for x ≥ 0.5 in α = 1 and 0.33, t =0.3 sec, is less than 5, whereas for α = 1 and 0.33, t =0.8 and 0.7 sec, the % error for x ≥ 0.4 is less than 8.

Suggested Citation

  • Nabard Habibi & Zohre Nouri, 2020. "Application of Local Fractional Homotopy Perturbation Method in Physical Problems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:2108973
    DOI: 10.1155/2020/2108973
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    References listed on IDEAS

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    6. Ming-Sheng Hu & Ravi P. Agarwal & Xiao-Jun Yang, 2012. "Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, December.
    7. Xiao-Jun Yang & Jordan Hristov & H. M. Srivastava & Bashir Ahmad, 2014. "Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, June.
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