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Solving Multi-Point Boundary Value Problems Using Sinc-Derivative Interpolation

Author

Listed:
  • Kenzu Abdella

    (Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar
    These authors contributed equally to this work.)

  • Jeet Trivedi

    (Department of Mathematics, Western University, London, ON N6A 5B7, Canada
    These authors contributed equally to this work.)

Abstract

In this paper, the Sinc-derivative collocation method is used to solve linear and nonlinear multi-point boundary value problems. This is done by interpolating the first derivative of the unknown variable via Sinc numerical methods and obtaining the desired solution through numerical integration of the interpolation and all higher order derivatives through successive differentiation of the interpolation. Non-homogeneous boundary conditions are reduced to homogeneous using suitable transformations. The efficiency and the accuracy of the method are tested using illustrative examples previously considered by other researchers who used different approaches. The results show the excellent performance of the Sinc-derivative collocation method.

Suggested Citation

  • Kenzu Abdella & Jeet Trivedi, 2020. "Solving Multi-Point Boundary Value Problems Using Sinc-Derivative Interpolation," Mathematics, MDPI, vol. 8(12), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2104-:d:450766
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    References listed on IDEAS

    as
    1. Dehghan, Mehdi, 2006. "Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 71(1), pages 16-30.
    2. Mehdi Dehghan & Mehdi Tatari, 2006. "The use of Adomian decomposition method for solving problems in calculus of variations," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-12, June.
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