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Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations

Author

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  • Mohamed M. Mousa

    (Department of Mathematics, College of Sciences and Human Studies at Hotat Sudair, Majmaah University, Al-Majmaah 11952, Saudi Arabia
    Department of Basic Engineering Sciences, Faculty of Engineering at Benha, Benha University, Benha 13512, Egypt)

  • Fahad Alsharari

    (Department of Mathematics, College of Sciences and Human Studies at Hotat Sudair, Majmaah University, Al-Majmaah 11952, Saudi Arabia
    Department of Mathematics, College of Science and Arts, Jouf University, Gurayat 77455, Saudi Arabia)

Abstract

In this work, the main concept of the homotopy perturbation method (HPM) was outlined and convergence theorems of the HPM for solving some classes of nonlinear integral, integro-differential and differential equations were proved. A theorem for estimating the error in the approximate solution was proved as well. The proposed HPM convergence theorems were confirmed and the efficiency of the technique was explored by applying the HPM for solving several classes of nonlinear integral/integro-differential equations.

Suggested Citation

  • Mohamed M. Mousa & Fahad Alsharari, 2021. "Convergence and Error Estimation of a New Formulation of Homotopy Perturbation Method for Classes of Nonlinear Integral/Integro-Differential Equations," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2244-:d:633946
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    References listed on IDEAS

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    1. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
    2. A. Harir & S. Melliani & H. El Harfi & L. S. Chadli, 2020. "Variational Iteration Method and Differential Transformation Method for Solving the SEIR Epidemic Model," International Journal of Differential Equations, Hindawi, vol. 2020, pages 1-7, July.
    3. Shumaila Javeed & Dumitru Baleanu & Asif Waheed & Mansoor Shaukat Khan & Hira Affan, 2019. "Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    4. Salah Abuasad & Ishak Hashim & Samsul Ariffin Abdul Karim, 2019. "Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-14, May.
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    Cited by:

    1. Naeem Saleem & Salman Furqan & Kinda Abuasbeh & Muath Awadalla, 2023. "Fuzzy Triple Controlled Metric like Spaces with Applications," Mathematics, MDPI, vol. 11(6), pages 1-30, March.

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