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Numerical Solution of Pantograph‐Type Delay Differential Equations Using Perturbation‐Iteration Algorithms

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  • M. Mustafa Bahşi
  • Mehmet Çevik

Abstract

The pantograph equation is a special type of functional differential equations with proportional delay. The present study introduces a compound technique incorporating the perturbation method with an iteration algorithm to solve numerically the delay differential equations of pantograph type. We put forward two types of algorithms, depending upon the order of derivatives in the Taylor series expansion. The crucial convenience of this method when compared with other perturbation methods is that this method does not require a small perturbation parameter. Furthermore, a relatively fast convergence of the iterations to the exact solutions and more accurate results can be achieved. Several illustrative examples are given to demonstrate the efficiency and reliability of the technique, even for nonlinear cases.

Suggested Citation

  • M. Mustafa Bahşi & Mehmet Çevik, 2015. "Numerical Solution of Pantograph‐Type Delay Differential Equations Using Perturbation‐Iteration Algorithms," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnljam:v:2015:y:2015:i:1:n:139821
    DOI: 10.1155/2015/139821
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    References listed on IDEAS

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    1. İhsan Timuçin Dolapçı & Mehmet Şenol & Mehmet Pakdemirli, 2013. "New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. İhsan Timuçin Dolapçı & Mehmet Şenol & Mehmet Pakdemirli, 2013. "New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, May.
    3. Hongliang Liu & Aiguo Xiao & Lihong Su, 2013. "Convergence of Variational Iteration Method for Second‐Order Delay Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Hongliang Liu & Aiguo Xiao & Lihong Su, 2013. "Convergence of Variational Iteration Method for Second-Order Delay Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, February.
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