Numerical methods for solving the multi-term time-fractional wave-diffusion equation
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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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RESEARCH ARTICLE Exact solution of two-term time-fractional Thornley's problem by operational method
TL;DR: In this article, a two-term time-fractional diffusion equation is studied, subject to a nonlocal boundary condition, and the fractional time derivatives are described in the Caputo sense.
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Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes
TL;DR: A fully-discrete scheme for 2D multi-term TFDWE is established and the approximation scheme is rigorously proved to be unconditionally stable via processing fractional derivative skillfully and the superclose result in broken H1-norm is deduced by utilizing special properties of quasi-Wilson element.
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An implicit difference scheme with the KPS preconditioner for two-dimensional time-space fractional convection-diffusion equations
TL;DR: It is proved under some suitable conditions that the derived difference scheme is stable and convergent, and the convergence orders of the scheme in time and space are given.
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A novel finite volume method for the nonlinear two-sided space distributed-order diffusion equation with variable coefficients
TL;DR: A novel finite volume method based on a piecewise-linear polynomial to discretize the problem and establish the Crank–Nicolson scheme is constructed and it is proved that the proposed method is stable and convergent with second order accuracy in both space and time.
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Finite difference scheme for simulating a generalized two-dimensional multi-term time fractional non-Newtonian fluid model
TL;DR: In this paper, a finite difference scheme based upon the Crank-Nicolson scheme is applied to the numerical approximation of a two-dimensional time fractional non-Newtonian fluid model.
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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Kai Diethelm,Neville J. Ford +1 more
TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
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