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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Temporal second-order difference methods for solving multi-term time fractional mixed diffusion and wave equations
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TL;DR: This article deals with an establishment and sharp theoretical analysis of a numerical scheme devised for solving the multi-dimensional multi-term time fractional mixed diffusion and wave equations and develops L2-1σ formula, used to numerically solve the time distributed-order diffusion andWave equations.
A novel finite volume method for the Riesz space distributed-order advection–diffusion equation
TL;DR: In this article, the authors investigated the finite volume method (FVM) for a distributed-order space-fractional advection-diffusion (AD) equation and proved that the Crank-Nicolson scheme is unconditionally stable and convergent with second-order accuracy.
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A novel finite element method for the distributed-order time fractional Cable equation in two dimensions
TL;DR: The unstructured mesh Galerkin finite element method with a weighted and shifted Grunwald difference approximation and Composite Trapezoid formula is presented to solve the nonhomogeneous two-dimensional distributed order time fractional Cable equation on irregular convex domains.
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A fast temporal second-order compact ADI difference scheme for the 2D multi-term fractional wave equation
Hong Sun,Zhi-zhong Sun +1 more
TL;DR: A fast temporal second-order compact ADI scheme is proposed for the 2D time multi-term fractional wave equation and the unconditional convergence and stability of the scheme in the discrete H 1 -norm are proved by the discrete energy method.
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A backward Euler difference scheme for the integro-differential equations with the multi-term kernels
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