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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Veröffentlicht in: | Advances in difference equations 2021-01, Vol.2021 (1), p.1-22, Article 4 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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 |