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An efficient fifth-order block method for solving third-order BVPs

Author

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  • Rufai, Mufutau Ajani
  • Carpentieri, Bruno
  • Ramos, Higinio

Abstract

This research paper introduces a new block method to solve third-order boundary-value problems (BVPs) directly. The method uses a suitable polynomial and three intermediate points to approximate the theoretical solution of third-order BVPs. An approximate solution is provided within the integration interval, and the basic properties of the proposed method, including convergence and stability, are theoretically analyzed. To assess the effectiveness of the proposed method, several real-life problems, such as boundary layer problems and physical model problems, are solved numerically. After comparison with some existing methods, the results of numerical experiments confirm the practical utility and effectiveness of the proposed method in real-world applications by demonstrating that it is superior and highly efficient in performance.

Suggested Citation

  • Rufai, Mufutau Ajani & Carpentieri, Bruno & Ramos, Higinio, 2024. "An efficient fifth-order block method for solving third-order BVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 307-321.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:307-321
    DOI: 10.1016/j.matcom.2024.04.014
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    References listed on IDEAS

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    1. Roul, Pradip & Prasad Goura, V.M.K., 2022. "A superconvergent B-spline technique for second order nonlinear boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    2. Ramos, Higinio & Singh, Gurjinder, 2022. "Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    3. Mohd Nasir, Nadirah & Abdul Majid, Zanariah & Ismail, Fudziah & Bachok, Norfifah, 2021. "Direct integration of the third-order two point and multipoint Robin type boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 411-427.
    4. Ross, I.M. & Proulx, R.J. & Borges, C.F., 2023. "A universal Birkhoff pseudospectral method for solving boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    5. Moghadam, Amin Abrishami & Soheili, Ali R. & Bagherzadeh, Amir Saboor, 2022. "Numerical solution of fourth-order BVPs by using Lidstone-collocation method," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    6. Costabile, F.A. & Gualtieri, M.I. & Napoli, A., 2021. "Lidstone-based collocation splines for odd-order BVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 124-135.
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