IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2013y2013i1n682537.html

New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations

Author

Listed:
  • İhsan Timuçin Dolapçı
  • Mehmet Şenol
  • Mehmet Pakdemirli

Abstract

In this paper, recently developed perturbation iteration method is used to solve Fredholm and Volterra integral equations. The study shows that the new method can be applied to both types of integral equations. Some numerical examples are given, and results are compared with other studies to illustrate the efficiency of the method.

Suggested Citation

  • İhsan Timuçin Dolapçı & Mehmet Şenol & Mehmet Pakdemirli, 2013. "New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:682537
    DOI: 10.1155/2013/682537
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/682537
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/682537?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Wang, Shu-Qiang & He, Ji-Huan, 2008. "Nonlinear oscillator with discontinuity by parameter-expansion method," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 688-691.
    2. Ji-Huan He, 2012. "Homotopy Perturbation Method with an Auxiliary Term," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, February.
    3. Ji-Huan He, 2012. "Homotopy Perturbation Method with an Auxiliary Term," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. M. Mustafa Bahşi & Mehmet Çevik, 2015. "Numerical Solution of Pantograph‐Type Delay Differential Equations Using Perturbation‐Iteration Algorithms," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lan Xu & Eric W. M. Lee, 2013. "Variational Iteration Method for the Magnetohydrodynamic Flow over a Nonlinear Stretching Sheet," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Y. Y. Lee, 2012. "Analysis of the Nonlinear Structural‐Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Hector Vazquez-Leal & Yasir Khan & Uriel Filobello-Nino & Arturo Sarmiento-Reyes & Alejandro Diaz-Sanchez & Luis-F. Cisneros-Sinencio, 2013. "Fixed‐Term Homotopy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Ali Akgül & Adem Kılıçman & Mustafa Inc, 2013. "Improved (G′/G)‐Expansion Method for the Space and Time Fractional Foam Drainage and KdV Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Muhammad Suleman & Qingbiao Wu, 2015. "Comparative Solution of Nonlinear Quintic Cubic Oscillator Using Modified Homotopy Perturbation Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    6. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Abdon Atangana & Dumitru Baleanu, 2013. "Nonlinear Fractional Jaulent‐Miodek and Whitham‐Broer‐Kaup Equations within Sumudu Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Asma Ali Elbeleze & Adem Kiliçman & Bachok M. Taib, 2012. "Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    9. El-Dib, Yusry O., 2021. "Homotopy perturbation method with rank upgrading technique for the superior nonlinear oscillation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 555-565.
    10. Zeng, De-Qiang, 2009. "Nonlinear oscillator with discontinuity by the max–min approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2885-2889.
    11. Zhang, Xiao & Yang, Chunxiao & Yang, Jinge, 2020. "Fast diffusion in a porous building material with a nonlocal source," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    12. Khudair, Ayad R. & Haddad, S.A.M. & khalaf, Sanaa L., 2017. "Restricted fractional differential transform for solving irrational order fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 81-85.
    13. Ramos, J.I., 2009. "An artificial parameter–Linstedt–Poincaré method for oscillators with smooth odd nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 380-393.
    14. Ji-Huan He, 2012. "Homotopy Perturbation Method with an Auxiliary Term," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    15. Kaya, M.O. & Altay Demirbağ, S., 2009. "Application of parameter expansion method to the generalized nonlinear discontinuity equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1967-1973.
    16. Tipu, Ghulam Hussain & Yao, Fengping & Anwar, Talha, 2025. "Bifurcation, chaos, and soliton dynamics in the integrable space curve model: A hybrid analytical and artificial neural network approach," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    17. Mehmet Şenol & İhsan Timuçin Dolapçı & Yiğit Aksoy & Mehmet Pakdemirli, 2013. "Perturbation‐Iteration Method for First‐Order Differential Equations and Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:682537. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.