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Solving Integro-Differential Boundary Value Problems Using Sinc-Derivative Collocation

Author

Listed:
  • Kenzu Abdella

    (Department of Mathematics, Statistics and Physics, Qatar University, P.O. Box 2173 Doha, Qatar
    These authors contributed equally to this work.)

  • Glen Ross

    (Department of Mathematics, Trent University, Peterborough, ON K9J 7B8, Canada
    These authors contributed equally to this work.)

Abstract

In this paper, the sinc-derivative collocation approach is used to solve second order integro-differential boundary value problems. While the derivative of the unknown variables is interpolated using sinc numerical methods, the desired solution and the integral terms are evaluated through numerical integration and all higher order derivatives are approximated through successive numerical differentiation. Suitable transformations are used to reduce non-homogeneous boundary conditions to homogeneous. Comparison of the proposed method with different approaches that were previously considered in the literature is carried out in order to test its accuracy and efficiency. The results show that the sinc-derivative collocation method performs well.

Suggested Citation

  • Kenzu Abdella & Glen Ross, 2020. "Solving Integro-Differential Boundary Value Problems Using Sinc-Derivative Collocation," Mathematics, MDPI, vol. 8(9), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1637-:d:417530
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    References listed on IDEAS

    as
    1. Sakran, M.R.A., 2019. "Numerical solutions of integral and integro-differential equations using Chebyshev polynomials of the third kind," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 66-82.
    2. Ahmad El-Ajou & Omar Abu Arqub & Shaher Momani, 2012. "Homotopy Analysis Method for Second-Order Boundary Value Problems of Integrodifferential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-18, September.
    3. M. Lakestani & M. Razzaghi & M. Dehghan, 2006. "Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-12, February.
    Full references (including those not matched with items on IDEAS)

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