Journal article Open Access
PARAMETER UNIFORM DISCRETIZATION OF SINGULARLY PERTURBED PARABOLIC DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS COEFFICIENTS AND LARGE DELAY
KENNA DIRIBI ABEBE
This study effort to introduce numerical method for parameter uniform discretization for singularly perturbed parabolic differential equations with discontinuous coefficient and large delay that implicate governing equation with interior layers over domain. Due to the presence of interior layers appearing in the solutions, the classical methods are unable to provide an efficient numerical solution unless they are applied with very fine meshes inside the regions. The comparison errors also given in tabular form and the work has been illustrated through examples for different values of small parameter ε. For the discretization of time derivative, we used the implicit Euler method on a uniform mesh and for the spatial discretization. Finally, maximum absolute errors for each examples was shown both by tables and graphs with different perturbation parameters and mesh sizes which shows betternment of the present method.
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- Publication date:
- May 12, 2025
- DOI:
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- License (for files):
- Creative Commons Attribution