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

Author

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  • 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
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    References listed on IDEAS

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    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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