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
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A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations
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TL;DR: This paper proposes and analyzes an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions using shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives.
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The Galerkin finite element method for a multi-term time-fractional diffusion equation
TL;DR: The initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain is considered and nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived.
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Fractional spectral collocation method
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A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations
TL;DR: An efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense.
References
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Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions
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