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A Sixth-Order Cubic B-Spline Approach for Solving Linear Boundary Value Problems: An In-Depth Analysis and Comparative Study

Author

Listed:
  • Ram Kishun Lodhi

    (Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune 412115, Maharashtra, India)

  • Moustafa S. Darweesh

    (Civil Engineering Department, College of Engineering, Northern Border University, Arar 73213, Saudi Arabia)

  • Abdelkarim Aydi

    (French International School Victor Hugo, Gontardstraße 11, 60488 Frankfurt am Main, Germany)

  • Lioua Kolsi

    (Department of Mechanical Engineering, College of Engineering, University of Ha’il, Ha’il City 81451, Saudi Arabia)

  • Anil Sharma

    (Department of Mathematics, University Institute of Sciences, Apex Institute of Technology—Computer Science and Engineering, Chandigarh University, Mohali 140413, Punjab, India)

  • Katta Ramesh

    (Department of Pure and Applied Mathematics, School of Mathematical Sciences, Sunway University, Bandar Sunway, Petaling Jaya 47500, Selangor, Malaysia
    Department of Mathematics, Graphic Era (Deemed to be University), Dehradun 248002, Uttarakhand, India
    Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara 144411, Punjab, India)

Abstract

This research presents an efficient and highly accurate cubic B-spline method (CBSM) for solving second-order linear boundary value problems (BVPs). The method achieves sixth-order convergence, supported by rigorous error analysis, ensuring rapid error reduction with mesh refinement. The effectiveness of the CBSM is validated through four numerical examples, showcasing its accuracy, reliability, and computational efficiency, making it well-suited for large-scale problems. A comparative analysis with existing methods confirms the superior performance of the CBSM, positioning it as a practical and powerful tool for solving second-order BVPs.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3274-:d:1501986
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    References listed on IDEAS

    as
    1. 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.
    2. Ishtiaq Ali & Muhammad Yaseen & Muhammad Abdullah & Sana Khan & Fethi Bin Muhammad Belgacem, 2023. "An Innovative Numerical Method Utilizing Novel Cubic B-Spline Approximations to Solve Burgers’ Equation," Mathematics, MDPI, vol. 11(19), pages 1-19, September.
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