Uniformly convergent numerical method for singularly perturbed convection‐diffusion type problems with nonlocal boundary condition

2020 ◽  
Vol 92 (12) ◽  
pp. 1914-1926
Author(s):  
Habtamu Garoma Debela ◽  
Gemechis File Duressa
Keyword(s):  
Boundary Condition ◽  
Numerical Method ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Convection Diffusion ◽  
Uniformly Convergent

scholarly journals Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Habtamu Garoma Debela
Keyword(s):  
Boundary Condition ◽  
Differential Equations ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Operator Method ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Convection Diffusion ◽  
Fitted Operator

This paper presents the study of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary condition. The proposed numerical scheme is a combination of the classical finite difference method for the boundary conditions and exponential fitted operator method for the differential equations at the interior points. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical examples considered. The method is shown to be first-order accuracy independent of the perturbation parameter ε .

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