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Numerical Solution of a Class of Functional‐Differential Equations Using Jacobi Pseudospectral Method

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  • A. H. Bhrawy
  • M. A. Alghamdi
  • D. Baleanu

Abstract

The shifted Jacobi‐Gauss‐Lobatto pseudospectral (SJGLP) method is applied to neutral functional‐differential equations (NFDEs) with proportional delays. The proposed approximation is based on shifted Jacobi collocation approximation with the nodes of Gauss‐Lobatto quadrature. The shifted Legendre‐Gauss‐Lobatto Pseudo‐spectral and Chebyshev‐Gauss‐Lobatto Pseudo‐spectral methods can be obtained as special cases of the underlying method. Moreover, the SJGLP method is extended to numerically approximate the nonlinear high‐order NFDE with proportional delay. Some examples are displayed for implicit and explicit forms of NFDEs to demonstrate the computation accuracy of the proposed method. We also compare the performance of the method with variational iteration method, one‐leg θ‐method, continuous Runge‐Kutta method, and reproducing kernel Hilbert space method.

Suggested Citation

  • A. H. Bhrawy & M. A. Alghamdi & D. Baleanu, 2013. "Numerical Solution of a Class of Functional‐Differential Equations Using Jacobi Pseudospectral Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:513808
    DOI: 10.1155/2013/513808
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    References listed on IDEAS

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    1. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    2. Mohammad Maleki & Ishak Hashim & Majid Tavassoli Kajani & Saeid Abbasbandy, 2012. "An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Changbo He & Xueqin Lv & Jing Niu, 2013. "A New Method Based on the RKHSM for Solving Systems of Nonlinear IDDEs with Proportional Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, April.
    4. Changbo He & Xueqin Lv & Jing Niu, 2013. "A New Method Based on the RKHSM for Solving Systems of Nonlinear IDDEs with Proportional Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Mohammad Maleki & Ishak Hashim & Majid Tavassoli Kajani & Saeid Abbasbandy, 2012. "An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, December.
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