Numerical methods for solving the multi-term time-fractional wave-diffusion equation
Reads0
Chats0
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
More filters
Journal ArticleDOI
Unsteady flow of viscoelastic fluid with the fractional K-BKZ model between two parallel plates
TL;DR: In this paper, the authors investigate the unsteady flow of a viscoelastic fluid between two parallel plates which is generated by the impulsively accelerated motion of the bottom plate.
Journal ArticleDOI
A formally second-order BDF finite difference scheme for the integro-differential equations with the multi-term kernels
TL;DR: A formally second-order backward differentiation formula (BDF) finite difference scheme is presented for the integro-differential equations with the multi-term kernels to construct a fully discrete difference scheme with the space discretization by the standard central difference formula.
Posted Content
A linearized second-order scheme for nonlinear time fractional Klein-Gordon type equations
Pin Lyu,Seakweng Vong +1 more
TL;DR: In this article, a linearized difference scheme for nonlinear time fractional Klein-Gordon type equations is proposed to solve the problem, which converges with second-order accuracy in time.
Journal ArticleDOI
Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations
Jingjun Zhao,Jingyu Xiao,Yang Xu +2 more
TL;DR: In this article, a finite element method (FEM) for multiterm fractional partial differential equations (MT-FPDEs) is studied for obtaining a numerical solution effectively.
Journal ArticleDOI
An unstructured mesh finite difference/finite element method for the three-dimensional time-space fractional Bloch-Torrey equations on irregular domains
TL;DR: The finite element method is used to solve the time-space fractional Bloch-Torrey equation on irregular domains in R 3 by adopting the L 2 − 1 σ approximation for the Caputo fractional derivative and a fully discrete scheme is presented.
References
More filters
Journal ArticleDOI
The random walk's guide to anomalous diffusion: a fractional dynamics approach
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.
Journal ArticleDOI
Analysis of Fractional Differential Equations
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.
Related Papers (5)
Finite difference/spectral approximations for the time-fractional diffusion equation
Yumin Lin,Chuanju Xu +1 more