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

In 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 directi...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2021; no. 1; pp. 1 - 22
Main Authors: Liu, Xiaomin, Abbas, Muhammad, Yang, Honghong, Qin, Xinqiang, Nazir, Tahir
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 06.01.2021
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications
Approximation
Cauchy–Schwarz inequality
Convection-diffusion equation
Difference and Functional Equations
Dimensional stability
Exponential basis function
Functional Analysis
Mathematics
Mathematics and Statistics
Methods
Numerical methods
Ordinary Differential Equations
Partial Differential Equations
Stability analysis
Tailored finite point method
Time-fractional convection-dominated diffusion equation
Topics in Special Functions and q-Special Functions: Theory
Two dimensional analysis
Time-fractional convection-dominated diffusion equation
65F50
Cauchy–Schwarz inequality
65F40
Tailored finite point method
Exponential basis function
65M06
26A33
65N06
35R11
65H10
65M12
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Description
Summary:In 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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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-03178-8