Hybrid difference scheme for singularly perturbed reaction-convection-diffusion problem with boundary and interior layers

2017 ◽  
Vol 314 ◽  
pp. 237-256 ◽  
Author(s):  
T. Prabha ◽  
M. Chandru ◽  
V. Shanthi
Keyword(s):  
Difference Scheme ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Convection Diffusion ◽  
Interior Layers ◽  
Boundary And Interior Layers

scholarly journals A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shifang Tian ◽  
Xiaowei Liu ◽  
Ran An
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Third Order ◽  
Order Accuracy ◽  
Convection Diffusion ◽  
Backward Euler

In this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and a hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform mesh and the backward Euler scheme are used for the temporal discretization. Furthermore, a preconditioning approach is also used to ensure uniform convergence. Numerical experiments show that the method is first-order accuracy in time and almost third-order accuracy in space.

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