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Numerical Investigation of Volterra Integral Equations of Second Kind using Optimal Homotopy Asymptotic Method

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  • Chu, Yu-Ming
  • Ullah, Saif
  • Ali, Muzaher
  • Tuzzahrah, Ghulam Fatima
  • Munir, Taj

Abstract

This investigation is concerned with the solutions of Volterra integral equations of second kind that have been determined by employing Optimal Homotopy Asymptotic method (OHAM). The existence and uniqueness of solutions are proved in this work. The obtained solutions are novel, and previous literature lacks such derivations. The convergence of the approximate solutions using the proposed method is investigated. Error’s estimation to the corresponding numerical scheme is also carried out. The reliability and accuracy of OHAM have been shown by comparison of our derived solutions with solutions obtained by other existing methods. The efficiency of the proposed numerical technique is exhibited through graphical illustrations, and results are drafted in tabular form for specific values of parameter to validate the numerical investigation.

Suggested Citation

  • Chu, Yu-Ming & Ullah, Saif & Ali, Muzaher & Tuzzahrah, Ghulam Fatima & Munir, Taj, 2022. "Numerical Investigation of Volterra Integral Equations of Second Kind using Optimal Homotopy Asymptotic Method," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003782
    DOI: 10.1016/j.amc.2022.127304
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    References listed on IDEAS

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    1. Jafar Biazar & Roya Montazeri, 2019. "Optimal Homotopy Asymptotic and Multistage Optimal Homotopy Asymptotic Methods for Solving System of Volterra Integral Equations of the Second Kind," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-17, January.
    2. Mohammad Almousa & Ahmad Ismail, 2013. "Optimal Homotopy Asymptotic Method for Solving the Linear Fredholm Integral Equations of the First Kind," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, July.
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    Cited by:

    1. Xu, Hang, 2023. "A generalized analytical approach for highly accurate solutions of fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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