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Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator

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  • Ramos, Higinio
  • Singh, Gurjinder

Abstract

This article deals with the development of an optimized third-derivative hybrid block method for integrating general second order two-point boundary value problems (BVPs) subject to different types of boundary conditions (BCs) such as Dirichlet, Neumann or Robin. A purely interpolation and collocation approach has been used in order to develop the method. A constructive approach has been applied in the development of the method to consider two off-step optimal points among an infinite number of possible choices in a two-step block corresponding to a generic interval of the form [xn,xn+2]. The obtained method simultaneously produces an approximate solution over the entire integration interval. Some numerical experiments have been presented that show the good performance of the presented scheme.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000467
    DOI: 10.1016/j.amc.2022.126960
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    References listed on IDEAS

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    1. Ramos, Higinio & Singh, Gurjinder, 2017. "A tenth order A-stable two-step hybrid block method for solving initial value problems of ODEs," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 75-88.
    2. Manni, Carla & Mazzia, Francesca & Sestini, Alessandra & Speleers, Hendrik, 2015. "BS2 methods for semi-linear second order boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 147-156.
    3. Ramos, Higinio & Rufai, M.A., 2018. "Third derivative modification of k-step block Falkner methods for the numerical solution of second order initial-value problems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 231-245.
    4. 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.
    5. Phang Pei See & Zanariah Abdul Majid & Mohamed Suleiman, 2014. "Three-Step Block Method for Solving Nonlinear Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, June.
    6. T. A. Biala & S. N. Jator, 2017. "A Family of Boundary Value Methods for Systems of Second-Order Boundary Value Problems," International Journal of Differential Equations, Hindawi, vol. 2017, pages 1-12, January.
    7. T. A. Biala, 2016. "A Computational Study of the Boundary Value Methods and the Block Unification Methods for," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-14, April.
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    Cited by:

    1. Tomar, Saurabh & Dhama, Soniya & Ramos, Higinio & Singh, Mehakpreet, 2023. "An efficient technique based on Green’s function for solving two-point boundary value problems and its convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 408-423.
    2. 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).
    3. 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.

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