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A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters

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  • Tariku Birabasa Mekonnen
  • Gemechis File Duressa
  • Niansheng Tang

Abstract

A numerical treatment via a difference scheme constructed by the Crank–Nicolson scheme for the time derivative and cubic spline in tension for the spatial derivatives on a layer resolving nonuniform Bakhvalov-type mesh for a singularly perturbed unsteady-state initial-boundary-value problem with two small parameters is presented. Error analysis of the constructed scheme is discussed and shown to be parameter-uniformly convergent with second-order convergence. Numerical experimentation is taken to confirm the theoretical findings.

Suggested Citation

  • Tariku Birabasa Mekonnen & Gemechis File Duressa & Niansheng Tang, 2022. "A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-11, February.
    • Handle: RePEc:hin:jijmms:5410754
    DOI: 10.1155/2022/5410754
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