May 12, 2025 Journal article Open Access

Tsige Assefa Faye

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  <dc:creator>Tsige Assefa Faye</dc:creator>
  <dc:date>2025-05-12</dc:date>
  <dc:description>This thesis deals with the numerical treatment of singularly perturbed delay differential equations. These singularly perturbed problems are described by differential equations in which the highest order derivative is multiplied by an arbitrarily small parameter (say) ε known as the singular perturbation parameter and containing a negative shift parameter. The presence of the perturbation parameter exhibits strong boundary layers in the solution. The abruptly changing behaviors of the solution in the layers make it very hard to solve the problem analytically. Standard numerical methods do not give satisfactory results unless a large mesh number is considered, which needs an enormous computational cost. So, one has to rely on suitable numerical methods to solve such types of problems. Therefore, it is important to develop robust numerical schemes for these problems. The main aim of this study is to develop and analyze a robust numerical method based on fitted techniques for solving singularly perturbed delay differential equations. The terms involving the delay are approximated using Taylors series approximation. Then, the resulting equation is solved by the fitted non-polynomial cubic spline method. It is shown that the method converges uniformly concerning the perturbation parameter. Numerical experiments have been carried out to corroborate the theoretical results. The layer behavior of the solutions is presented using tables and graphs and observed to agree with the existing theories. The error analysis of the scheme is done and observed that the proposed method is parameter uniform convergent with the order of convergence (h 2 ). To validate the applicability of the proposed method the obtained results were compared to some methods that appear in the literature. The comparison shows that the proposed method provides better results than some results available in the literature.</dc:description>
  <dc:identifier>https://zenodo.org/record/6275</dc:identifier>
  <dc:identifier>10.20372/nadre:6275</dc:identifier>
  <dc:identifier>oai:zenodo.org:6275</dc:identifier>
  <dc:relation>doi:10.20372/nadre:6274</dc:relation>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>http://www.opendefinition.org/licenses/cc-by</dc:rights>
  <dc:title>Numerical Treatment of Singularly Perturbed Differential Equation Having Small Delays</dc:title>
  <dc:type>info:eu-repo/semantics/article</dc:type>
  <dc:type>publication-article</dc:type>
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