scholarly journals Higher Order Fitted Operator Finite Difference Method for Two-Parameter Parabolic Convection-Diffusion Problems

2019 ◽  
Vol 11 (4) ◽  
pp. 455-467
Author(s):  
Tesfaye Bullo ◽  
Gemechis Duressa ◽  
Guy DEGLA
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Higher Order ◽  
Convection Diffusion ◽  
Fitted Operator ◽  
Two Parameter ◽  
Diffusion Problems

Robust Finite Difference Method for Singularly Perturbed Two-Parameter Parabolic Convection-Diffusion Problems

2020 ◽  
pp. 2050034
Author(s):  
Tesfaye Aga Bullo ◽  
Gemechis File Duressa ◽  
Guy Aymard Degla
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Perturbation Parameter ◽  
Accurate Solution ◽  
Singularly Perturbed ◽  
Parabolic Problems ◽  
Uniform Mesh ◽  
Convection Diffusion ◽  
Diffusion Problems

Robust finite difference method is introduced in order to solve singularly perturbed two parametric parabolic convection-diffusion problems. In order to discretize the solution domain, Micken’s type discretization on a uniform mesh is applied and then followed by the fitted operator approach. The convergence of the method is established and observed to be first-order convergent, but it is accelerated by Richardson extrapolation. To validate the applicability of the proposed method, some numerical examples are considered and observed that the numerical results confirm the agreement of the method with the theoretical results effectively. Furthermore, the method is convergent regardless of perturbation parameter and produces more accurate solution than the standard methods for solving singularly perturbed parabolic problems.

scholarly journals Fitted Operator Finite Difference Method for Singularly Perturbed Parabolic Convection-Diffusion Type

2021 ◽  
Vol 5 (1) ◽  
pp. 1-14
Author(s):  
Tesfaye Aga Bullo ◽  
Gemechis File Duressa
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Spatial Direction ◽  
Convection Diffusion ◽  
Backward Euler ◽  
Numerical Experimentation ◽  
Fitted Operator

In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson extrapolation method is applied on the time direction and the fitted operator finite difference method on the spatial direction is used, on the uniform grids. The stability and consistency of the method were established very well to guarantee the convergence of the method. Numerical experimentation is carried out on model examples, and the results are presented both in tables and graphs. Further, the present method gives a more accurate solution than some existing methods reported in the literature.

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