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An Efficient Third-Derivative Hybrid Block Method for the Solution of Second-Order BVPs

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  • Mufutau Ajani Rufai

    (Department of Mathematics, University of Bari, Aldo Moro, 70125 Bari, Italy)

Abstract

A new one-step hybrid block method with two-point third derivatives is developed to solve the second-order boundary value problems (BVPs). The mathematical derivation of the proposed method is based on the interpolation and collocation methods. The theoretical properties of the proposed method, such as consistency and convergence, are well analysed. Some BVPs with different boundary conditions are solved to demonstrate the efficiency and feasibility of the suggested method. The numerical results of the proposed method are much closer to the exact solutions and more competitive than other numerical methods in the available literature.

Suggested Citation

  • Mufutau Ajani Rufai, 2022. "An Efficient Third-Derivative Hybrid Block Method for the Solution of Second-Order BVPs," Mathematics, MDPI, vol. 10(19), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3692-:d:936724
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    References listed on IDEAS

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    1. 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).
    2. Tafakkori–Bafghi, M. & Loghmani, G.B. & Heydari, M., 2022. "Numerical solution of two-point nonlinear boundary value problems via Legendre–Picard iteration method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 133-159.
    3. Ramos, Higinio & Rufai, M.A., 2019. "A third-derivative two-step block Falkner-type method for solving general second-order boundary-value systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 139-155.
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