Finite difference/spectral approximations for the time-fractional diffusion equation
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Summary
It is proved that the full discretization is unconditionally stable, and the numerical solution converges to the exact one with order O(@Dt^2^-^@a+N^- ^m), where @Dt,N and m are the time step size, polynomial degree, and regularity of the exact solution respectively.
- Type
- article
- Published
- 2007-08-01
- Cited by
- 1,841
- References
- 23
- OpenAlex
- https://openalex.org/W2165076033
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:40378825
Keywords
Mathematics, Discretization, Legendre polynomials, Diffusion equation, Fractional calculus
References
- Time Fractional Diffusion: A Discrete Random Walk Approach
- Solution for a Fractional Diffusion-Wave Equation Defined in a Bounded Domain
- Approximations spectrales de problèmes aux limites elliptiques
- Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation
- Fractals and fractional calculus in continuum mechanics
- Numerical Solution of the Bagley-Torvik Equation
- Numerical Approximation of Partial Differential Equations
- Fractional diffusion and wave equations
- Least squares finite-element solution of a fractional order two-point boundary value problem
- Numerical methods for the solution of partial difierential equations of fractional order
- Time fractional advection-dispersion equation
- Analysis of iterative methods for the viscous/inviscid coupled problem via a spectral element approximation
- The fractional diffusion equation
- Numerical Solution of Fractional Advection-Dispersion Equation
- A finite difference scheme for partial integro-differential equations with a weakly singular kernel
- Wright functions as scale-invariant solutions of the diffusion-wave equation
- A second-order accurate numerical approximation for the fractional diffusion equation
- Finite difference approximations for fractional advection-dispersion flow equations
- Properties of the Mittag-Leffler Relaxation Function
- Asymptotic correction and inverse eigenvalue problems: an overview
Cited by
- Finite volume methods for simulating anomalous transport
- Novel analytical and numerical methods for solving fractional dynamical systems
- A Wavelet Numerical Method for Solving Nonlinear Fractional Vibration, Diffusion and Wave Equations
- A new Quarter-Sweep Arithmetic Mean (QSAM) method to solve diffusion equations
- Membrane Capacitive Memory Alters Spiking in Neurons Described by the Fractional-Order Hodgkin-Huxley Model
- DMLPG solution of the fractional advection–diffusion problem
- A numerical method based on fully discrete direct discontinuous Galerkin method for the time fractional diffusion equation
- Finite difference/finite element method for a nonlinear time-fractional fourth-order reaction-diffusion problem
- The method of approximate particular solutions for the time-fractional diffusion equation with a non-local boundary condition
- Two high-order numerical algorithms for solving the multi-term time fractional diffusion-wave equations
- Three-point combined compact difference schemes for time-fractional advection-diffusion equations with smooth solutions
- Numerical Algorithms with High Spatial Accuracy for the Fourth-Order Fractional Sub-Diffusion Equations with the First Dirichlet Boundary Conditions
- Fast numerical solution for fractional diffusion equations by exponential quadrature rule
- Two Alternating Direction Implicit Difference Schemes for Two-Dimensional Distributed-Order Fractional Diffusion Equations
- Modeling and simulation of the fractional space-time diffusion equation
- Time-Splitting Schemes for Fractional Differential Equations I: Smooth Solutions
- Numerical Solution of Space-Time Fractional Convection-Diffusion Equations with Variable Coefficients Using Haar Wavelets
- Revisited Fisher’s equation in a new outlook: A fractional derivative approach
- Sobre cálculo fracionário e soluções da equação de Bessel
- Numerical analysis and simulations for phase-field equations
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