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 high-order spectral method for the multi-term time-fractional diffusion equations
TL;DR: Based on the space-time spectral method, a high-order scheme is proposed in this paper, where the Legendre polynomials are adopted in temporal discretization and the Fourier-like basis functions are constructed for spatial discretisation.
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Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions☆
TL;DR: In this article, a modified weighted shifted Grunwald-Letnikov (WSGL) formula was proposed to solve multi-term fractional ordinary and partial differential equations, and the linear stability and second-order convergence for both smooth and non-smooth solutions when the regularity of the solutions is known.
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Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping
TL;DR: The unconditional stability and convergence with order O ( ? 6 - 2 α ) are proved, where ? is time stepping and the MLRPI scheme based on Galerkin weak form is analyzed.
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Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains
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TL;DR: An implicit scheme for the numerical approximation of the distributed order time-fractional reaction-diffusion equation with a nonlinear source term is presented and the stability and the convergence order are analysed and illustrated.
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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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