IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2022y2022i1n2217882.html

Approximation Technique for Solving Linear Volterra Integro‐Differential Equations with Boundary Conditions

Author

Listed:
  • Mohamed E. A. Alnair
  • Ahmed A. Khidir

Abstract

This paper presents a new technique for solving linear Volterra integro‐differential equations with boundary conditions. The method is based on the blending of the Chebyshev spectral methods. The application of the proposed method leads the Volterra integro‐differential equation to a system of algebraic equations that are easy to solve. Some examples are introduced and the obtained results are compared with exact solution as well as the methods that reported in the literature to illustrate the effectiveness and accuracy of the method. The results demonstrate that there is congruence between the numerical and the exact results to a high order of accuracy. Tables were generated to verify the accuracy convergence of the method and error. Figures are presented to show the excellent agreement between the results of this study and the results from literature.

Suggested Citation

  • Mohamed E. A. Alnair & Ahmed A. Khidir, 2022. "Approximation Technique for Solving Linear Volterra Integro‐Differential Equations with Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlaaa:v:2022:y:2022:i:1:n:2217882
    DOI: 10.1155/2022/2217882
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/2217882
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/2217882?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. M. Higazy & Sudhanshu Aggarwal & Taher A. Nofal & Hijaz Ahmad, 2020. "Sawi Decomposition Method for Volterra Integral Equation with Application," Journal of Mathematics, Hindawi, vol. 2020, pages 1-13, December.
    2. Mirzaee, Farshid & Solhi, Erfan & Naserifar, Shiva, 2021. "Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    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. Ahmed A. Khidir, 2023. "The Spectral Adomian Decomposition Method for the Solution of MHD Jeffery–Hamel Problem," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(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. Mamta Kapoor & Nehad Ali Shah & Salman Saleem & Wajaree Weera, 2022. "An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions," Mathematics, MDPI, vol. 10(12), pages 1-26, June.
    2. DianJu Qiao & ZhenWei Zhang & FangHao Liu & Bo Sun, 2022. "Location Optimization Model of a Greenhouse Sensor Based on Multisource Data Fusion," Complexity, John Wiley & Sons, vol. 2022(1).
    3. Ahmadinia, M. & Afshariarjmand, H. & Salehi, M., 2023. "Numerical solution of multi-dimensional Itô Volterra integral equations by the second kind Chebyshev wavelets and parallel computing process," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    4. Zare, Farideh & Heydari, Mohammad & Loghmani, Ghasem Barid, 2024. "Convergence analysis of an iterative scheme to solve a family of functional Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    5. Singh, P.K. & Saha Ray, S., 2023. "An efficient numerical method based on Lucas polynomials to solve multi-dimensional stochastic Itô-Volterra integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 826-845.
    6. Muhammad Nadeem & Mouad M. H. Ali, 2022. "Two Computational Strategies for the Approximate Solution of the Nonlinear Gas Dynamic Equations," Journal of Mathematics, John Wiley & Sons, vol. 2022(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:jnlaaa:v:2022:y:2022:i:1:n:2217882. 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/4058 .

    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.