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Three-Step Block Method for Solving Nonlinear Boundary Value Problems

Author

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  • Phang Pei See
  • Zanariah Abdul Majid
  • Mohamed Suleiman

Abstract

We propose a three-step block method of Adam’s type to solve nonlinear second-order two-point boundary value problems of Dirichlet type and Neumann type directly. We also extend this method to solve the system of second-order boundary value problems which have the same or different two boundary conditions. The method will be implemented in predictor corrector mode and obtain the approximate solutions at three points simultaneously using variable step size strategy. The proposed block method will be adapted with multiple shooting techniques via the three-step iterative method. The boundary value problem will be solved without reducing to first-order equations. The numerical results are presented to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:379829
    DOI: 10.1155/2014/379829
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    Cited by:

    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).

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