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Solving Linear Second-Order Singularly Perturbed Differential Difference Equations via Initial Value Method

Author

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  • Wondwosen Gebeyaw Melesse
  • Awoke Andargie Tiruneh
  • Getachew Adamu Derese

Abstract

In this paper, an initial value method for solving a class of linear second-order singularly perturbed differential difference equation containing mixed shifts is proposed. In doing so, first, the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay and advance parameters using Taylor series expansion. From the modified problem, two explicit initial value problems which are independent of the perturbation parameter are produced; namely, the reduced problem and the boundary layer correction problem. These problems are then solved analytically and/or numerically, and those solutions are combined to give an approximate solution to the original problem. An error estimate for this method is derived using maximum norm. Several test problems are considered to illustrate the theoretical results. It is observed that the present method approximates the exact solution very well.

Suggested Citation

  • Wondwosen Gebeyaw Melesse & Awoke Andargie Tiruneh & Getachew Adamu Derese, 2019. "Solving Linear Second-Order Singularly Perturbed Differential Difference Equations via Initial Value Method," International Journal of Differential Equations, Hindawi, vol. 2019, pages 1-10, November.
    • Handle: RePEc:hin:jnijde:5259130
    DOI: 10.1155/2019/5259130
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    Cited by:

    1. Gemechis File Duressa & Imiru Takele Daba & Chernet Tuge Deressa, 2023. "A Systematic Review on the Solution Methodology of Singularly Perturbed Differential Difference Equations," Mathematics, MDPI, vol. 11(5), pages 1-16, February.

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