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Modified Homotopy Perturbation Method for Fredholm–Volterra Integro-Differential Equation

In: Recent Advances in Mathematical Sciences

Author

Listed:
  • F. S. Zulkarnain

    (Universiti Putra Malaysia (UPM), Faculty of Science, Departments of Mathematics)

  • Z. K. Eshkuvatov

    (Universiti Sains ISlam Malaysia (USIM), Faculty of Science and Technology)

  • N. M. A. Nik Long

    (Universiti Putra Malaysia (UPM), Institute for Mathematical Research)

  • F. Ismail

    (Universiti Putra Malaysia (UPM), Faculty of Science, Departments of Mathematics)

Abstract

In this paper, consider a linear Fredholm–Volterro integro-differential equation (FVIDE) of the third kind has derivative of order m where m is positive integer. This type of integral has been solved by using modified homotopy perturbation method (HPM) to get approximate solutions. In this modification, selective functions and unknown parameters are introduced to help us obtain only two-step iterations. This proposed method could avoid common problems such as complex and long calculations. It is found that modified HPM is a semi-analytical method and easy to apply for solving FVIDE. Numerical examples are given to present the efficiency and reliability of the propose method.

Suggested Citation

  • F. S. Zulkarnain & Z. K. Eshkuvatov & N. M. A. Nik Long & F. Ismail, 2016. "Modified Homotopy Perturbation Method for Fredholm–Volterra Integro-Differential Equation," Springer Books, in: Adem Kılıçman & Hari M. Srivastava & M. Mursaleen & Zanariah Abdul Majid (ed.), Recent Advances in Mathematical Sciences, pages 37-44, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-0519-0_4
    DOI: 10.1007/978-981-10-0519-0_4
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