scholarly journals An explicit solution of an L1 approximation problem

1985 ◽  
Vol 44 (2) ◽  
pp. 194-195
Author(s):  
D Kershaw
Keyword(s):  
Explicit Solution ◽  
Approximation Problem ◽  
L1 Approximation

scholarly journals Novel finite point approach for solving time-fractional convection-dominated diffusion equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xiaomin Liu ◽  
Muhammad Abbas ◽  
Honghong Yang ◽  
Xinqiang Qin ◽  
Tahir Nazir
Keyword(s):  
Variable Coefficients ◽  
Numerical Dispersion ◽  
Discrete Equation ◽  
Finite Point ◽  
Spatial Direction ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Tailored Finite Point Method ◽  
L1 Approximation ◽  
The Stability

AbstractIn this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with variable coefficients. The tailored finite point method (TFPM) is adopted to discrete equation in the spatial direction, while the time direction is discreted by the G-L approximation and the L1 approximation. It can effectively eliminate non-physical oscillation or excessive numerical dispersion caused by convection dominant. The stability of the scheme is verified by theoretical analysis. Finally, one-dimensional and two-dimensional numerical examples are presented to verify the efficiency of the method.

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