The Finite Volume Element Method for Time Fractional Generalized Burgers’ Equation

The Finite Volume Element Method for Time Fractional Generalized Burgers’ Equation

In this paper, we use the finite volume element method (FVEM) to approximate a one-dimensional, time fractional generalized Burgers’ equation. We construct the fully discrete finite volume element scheme for this equation by approximating the time fractional derivative term by the L1 formula and app...

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Veröffentlicht in:Fractal and fractional 2024-01, Vol.8 (1), p.53
Hauptverfasser: Zhang, Jingru, Yang, Qing
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Burgers equation
convergence
Differential equations
finite volume element method
Fluid dynamics
Methods
numerical simulation
Ordinary differential equations
Partial differential equations
time fractional generalized Burgers’ equation
Wave propagation
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Beschreibung
Zusammenfassung:In this paper, we use the finite volume element method (FVEM) to approximate a one-dimensional, time fractional generalized Burgers’ equation. We construct the fully discrete finite volume element scheme for this equation by approximating the time fractional derivative term by the L1 formula and approximating the spatial terms using FVEM. The convergence of the scheme is proven. Finally, numerical examples are provided to confirm the scheme’s validity.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract8010053