IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i6p508-d236872.html
   My bibliography  Save this article

Numerical Solution of the Boundary Value Problems Arising in Magnetic Fields and Cylindrical Shells

Author

Listed:
  • Aasma Khalid

    (Department of Mathematics, Government College University Faisalabad, Faisalabad 38023, Pakistan
    Department of Mathematics, Government College Women University Faisalabad, Faisalabad 38023, Pakistan)

  • Muhammad Nawaz Naeem

    (Department of Mathematics, Government College University Faisalabad, Faisalabad 38023, Pakistan)

  • Zafar Ullah

    (Department of Mathematics, University of Education, Campus DG Khan, Lahore 54770, Pakistan)

  • Abdul Ghaffar

    (Department of Mathematics, Balochistan University of Information Technology, Engineering and Management Sciences (BUITEMS), Quetta 87300, Pakistan)

  • Dumitru Baleanu

    (Department of Mathematics, Cankaya University, Ankara 06530, Turkey
    Institute of Space Sciences, Magurele-Bucharest 077125, Romania)

  • Kottakkaran Sooppy Nisar

    (Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia)

  • Maysaa M. Al-Qurashi

    (Department of Mathematics, King Saud University, Riyadh 11495, Saudi Arabia)

Abstract

This paper is devoted to the study of the Cubic B-splines to find the numerical solution of linear and non-linear 8th order BVPs that arises in the study of astrophysics, magnetic fields, astronomy, beam theory, cylindrical shells, hydrodynamics and hydro-magnetic stability, engineering, applied physics, fluid dynamics, and applied mathematics. The recommended method transforms the boundary problem to a system of linear equations. The algorithm we are going to develop in this paper is not only simply the approximation solution of the 8th order BVPs using Cubic-B spline but it also describes the estimated derivatives of 1st order to 8th order of the analytic solution. The strategy is effectively applied to numerical examples and the outcomes are compared with the existing results. The method proposed in this paper provides better approximations to the exact solution.

Suggested Citation

  • Aasma Khalid & Muhammad Nawaz Naeem & Zafar Ullah & Abdul Ghaffar & Dumitru Baleanu & Kottakkaran Sooppy Nisar & Maysaa M. Al-Qurashi, 2019. "Numerical Solution of the Boundary Value Problems Arising in Magnetic Fields and Cylindrical Shells," Mathematics, MDPI, vol. 7(6), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:508-:d:236872
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/6/508/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/6/508/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Muhammad Aslam Noor & Syed Tauseef Mohyud-Din, 2008. "Variational Homotopy Perturbation Method for Solving Higher Dimensional Initial Boundary Value Problems," Mathematical Problems in Engineering, Hindawi, vol. 2008, pages 1-11, June.
    2. Mingzhu Li & Lijuan Chen & Qiang Ma, 2013. "The Numerical Solution of Linear Sixth Order Boundary Value Problems with Quartic B-Splines," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, December.
    3. Yu-Xi Wang & Hua-You Si & Lu-Feng Mo, 2008. "Homotopy Perturbation Method for Solving Reaction-Diffusion Equations," Mathematical Problems in Engineering, Hindawi, vol. 2008, pages 1-5, April.
    4. Muhammad Aslam Noor & Syed Tauseef Mohyud-Din, 2008. "Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials," Mathematical Problems in Engineering, Hindawi, vol. 2008, pages 1-12, March.
    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. Ram Kishun Lodhi & Moustafa S. Darweesh & Abdelkarim Aydi & Lioua Kolsi & Anil Sharma & Katta Ramesh, 2024. "A Sixth-Order Cubic B-Spline Approach for Solving Linear Boundary Value Problems: An In-Depth Analysis and Comparative Study," Mathematics, MDPI, vol. 12(20), pages 1-16, October.

    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. Xin Song & Rui Wu, 2024. "An Efficient Numerical Method for Solving a Class of Nonlinear Fractional Differential Equations and Error Estimates," Mathematics, MDPI, vol. 12(12), pages 1-12, June.
    2. Nawal AL-Zaid & Amani AL-Refaidi & Huda Bakodah & Mariam AL-Mazmumy, 2022. "Solution of Second- and Higher-Order Nonlinear Two-Point Boundary-Value Problems Using Double Decomposition Method," Mathematics, MDPI, vol. 10(19), pages 1-15, September.

    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:gam:jmathe:v:7:y:2019:i:6:p:508-:d:236872. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.