Numerical methods for solving the multi-term time-fractional wave-diffusion equation
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TLDR
Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations and can be extended to other kinds of themulti-term fractional time-space models with fractional Laplacian.Abstract:
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.read more
Citations
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A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements
TL;DR: A fully discrete numerical scheme derived using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time is applied to solve the multi-term time and space fractional Bloch-Torrey equation.
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A numerical investigation of the time distributed-order diffusion model
TL;DR: In this article, the authors approximate the distributed-order fractional model with a multi-term fractional approach, which is then solved by an implicit numerical method, and demonstrate the effectiveness of the method and to exhibit the solution behavior of different diffusion models.
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A Weak Galerkin Finite Element Method for Multi-Term Time-Fractional Diffusion Equations
TL;DR: The stability and convergence of a weak Galerkin finite element method for multi-term time-fractional diffusion equations with one-dimensional space variable are proved.
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Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative
TL;DR: In this paper, the local fractional Laplace variational iteration method was applied to solve the linear LF PDE, and the non-differentiable approximate solutions were obtained and their graphs were also shown.
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An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations
TL;DR: In this paper, an alternating direction implicit (ADI) spectral method is developed based on Legendre spectral approximation in space and finite difference discretization in time for the initial boundary value problem of the two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations.
References
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Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
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