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
Exponentially fitted methods for solving time fractional nonlinear reaction-diffusion equation
TL;DR: The proposed methods are proved to be unconditionally stable and convergent by Fourier analysis, and the effectiveness of the numerical scheme is confirmed by numerical test problems and a comparison with other methods is presented.
Journal ArticleDOI
An efficient Hamiltonian numerical model for a fractional Klein–Gordon equation through weighted-shifted Grünwald differences
TL;DR: In this paper, the authors investigated numerically a nonlinear wave equation with fractional derivatives of the Riesz type in space and proposed a discrete energy function that estimates the continuous counterpart and which is preserved under the same conditions.
Book ChapterDOI
Chapter 8 – Numerical Methods
TL;DR: In this article, several modified Fourier's heat conduction laws and modified Darcy's diffusion laws are proposed for power law non-Newtonian fluids and fractional Maxwell viscoelastic fluid subject to various physical regimes and the fractional convection diffusion in a comb-like structure with Cattaneo Christov flux.
Journal ArticleDOI
Two-dimensional Bernoulli wavelets with satisfier function in the Ritz–Galerkin method for the time fractional diffusion-wave equation with damping
TL;DR: In this article, the two-dimensional Bernoulli wavelets with Ritz-Galerkin method are applied for the numerical solution of the time fractional diffusion-wave equation, and a satisfier function which satisfies all the initial and boundary conditions is derived.
Journal ArticleDOI
Multistep schemes for one and two dimensional electromagnetic wave models based on fractional derivative approximation
TL;DR: The proposed multistep schemes transform the FDMEWs into the tridiagonal system for 1D case and pentagon system for 2D case which support the theoretical findings for both 1D and 2D cases.
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