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| Content Provider | Springer Nature : BioMed Central |
|---|---|
| Author | Hassen, Zerihun Ibrahim Duressa, Gemechis File |
| Abstract | Objective In this work, singularly perturbed time dependent delay parabolic convection-diffusion problem with Dirichlet boundary conditions is considered. The solution of this problem exhibits boundary layer at the right of special domain. In this layer the solution experiences steep gradients or oscillation so that traditional numerical methods may fail to provide smooth solutions. We developed oscillation free parameter uniform exponentially spline numerical method to solve the considered problem. Results In the temporal direction, the implicit Euler method is applied, and in the spatial direction, an exponential spline method with uniform mesh is applied. To handle the effect of perturbation parameter, an exponential fitting factor is introduced. For the developed numerical scheme, stability and uniform error estimates are examined. It is shown that the scheme is uniformly convergent of linear order in the maximum norm. Numerical examples are provided to illustrate the theoretical findings. |
| Related Links | https://bmcresnotes.biomedcentral.com/counter/pdf/10.1186/s13104-024-07005-1.pdf |
| Ending Page | 14 |
| Page Count | 14 |
| Starting Page | 1 |
| File Format | HTM / HTML |
| ISSN | 17560500 |
| DOI | 10.1186/s13104-024-07005-1 |
| Journal | BMC Research Notes |
| Issue Number | 1 |
| Volume Number | 18 |
| Language | English |
| Publisher | BioMed Central |
| Publisher Date | 2025-01-20 |
| Access Restriction | Open |
| Subject Keyword | Biomedicine Medicine Public Health Life Sciences Exponential spline Oscillation-free Singularly perturbed delay problem Fitting factor Convection-diffusion Uniform convergence 65M06 65M12 65M15 Medicine/Public Health |
| Content Type | Text |
| Resource Type | Article |
| Subject | Biochemistry, Genetics and Molecular Biology Medicine |
| Journal Impact Factor | 1.6/2023 |
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