An Unconditionally Stable Laguerre Based Finite Difference Method for Transient Diffusion and Convection-Diffusion Problems

2019 ◽  
Vol 12 (3) ◽  
pp. 681-708
Author(s):  
Wescley T. B. de Sousa and Carlos F. T. Matt
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Unconditionally Stable ◽  
Convection Diffusion ◽  
Transient Diffusion ◽  
Diffusion And Convection ◽  
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.

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