An efficient numerical technique for a specific family of singularly perturbed boundary value problems

Document Type : Research Paper

Authors

Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran

Abstract

This paper deals with a particular family of singularly perturbed two-point boundary value problems characterized by the perturbation parameter $0<\varepsilon\ll 1$, and it introduces a new numerical technique to approximate its solution. As the perturbation parameter $\varepsilon$ decreases, the majority of classic numerical methods that utilize uniform grids necessitate significantly reduced step sizes. Consequently, we employ a non-equidistant mesh. After discretizing the problem and constructed some high order compact methods, the original problem is transformed into a linear algebraic system. Also, it is demonstrated that the present method converges with order $4$ in $L_\infty$ norm. Finally, numerical simulations will demonstrate the efficacy of the proposed method and confirm the theoretical results.

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References

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History

  • Receive Date: 05 October 2024
  • Revise Date: 03 April 2025
  • Accept Date: 06 May 2025

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