A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative
2015
A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite difference method is derived. The stability of this scheme is established by von Neumann analysis. Some numerical results are shown, which demonstrate the efficiency and convergence of the method. Additionally, some physical properties of this fractional diffusion system are simulated, which further confirm the effectiveness of our method.
Keywords:
- Numerical analysis
- Riemann hypothesis
- Mathematical analysis
- Finite difference method
- Mathematical optimization
- Fractional calculus
- Weighted arithmetic mean
- Diffusion equation
- Von Neumann stability analysis
- Discretization
- Mathematics
- fractional diffusion
- riemann liouville
- Convergence (routing)
- Von Neumann architecture
- Correction
- Source
- Cite
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