This study explores the numerical method of 1-D singularly perturbed parabolic problems, influenced by two distinct parameters affecting diffusion and convection. With discontinuous convection and source terms, the solutions exhibit boundary and interior layers due to the perturbations and discontinuities. The time variable is first discretized using the implicit Euler method on a uniform mesh, followed by spatial discretization of the semi-discrete problems with a non-polynomial cubic spline incorporating an exponential fitting factor. The method is shown to be first-order accurate and uniformly convergent. Its efficiency is demonstrated through four test cases, yielding more precise results than those reported in existing methods.
Cheru, S. Lema , Duressa, G. File and Mekonnen, T. Birabasa (2025). ROBUST NUMERICAL APPROACH FOR SINGULARLY PERTURBED PARABOLIC PROBLEMS WITH DISCONTINUOUS CONVECTION COEFFICIENTS AND SOURCE TERMS. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.63426.2831
MLA
Cheru, S. Lema, , Duressa, G. File, and Mekonnen, T. Birabasa. "ROBUST NUMERICAL APPROACH FOR SINGULARLY PERTURBED PARABOLIC PROBLEMS WITH DISCONTINUOUS CONVECTION COEFFICIENTS AND SOURCE TERMS", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.63426.2831
HARVARD
Cheru, S. Lema, Duressa, G. File, Mekonnen, T. Birabasa (2025). 'ROBUST NUMERICAL APPROACH FOR SINGULARLY PERTURBED PARABOLIC PROBLEMS WITH DISCONTINUOUS CONVECTION COEFFICIENTS AND SOURCE TERMS', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.63426.2831
CHICAGO
S. Lema Cheru , G. File Duressa and T. Birabasa Mekonnen, "ROBUST NUMERICAL APPROACH FOR SINGULARLY PERTURBED PARABOLIC PROBLEMS WITH DISCONTINUOUS CONVECTION COEFFICIENTS AND SOURCE TERMS," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.63426.2831
VANCOUVER
Cheru, S. Lema, Duressa, G. File, Mekonnen, T. Birabasa ROBUST NUMERICAL APPROACH FOR SINGULARLY PERTURBED PARABOLIC PROBLEMS WITH DISCONTINUOUS CONVECTION COEFFICIENTS AND SOURCE TERMS. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.63426.2831
)