Journal Article10.1016/J.CNSNS.2020.105432
A fourth-order dissipation-preserving algorithm with fast implementation for space fractional nonlinear damped wave equations
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TL;DR: A novel high-accuracy dissipation-preserving finite difference scheme is constructed by using the new fourth-order fractional central difference operator using the toeplitz-like differentiation matrix and the computation efficiency is raised by fast Fourier transform.
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About: This article is published in Communications in Nonlinear Science and Numerical Simulation. The article was published on 01 Dec 2020. The article focuses on the topics: Finite difference method & Finite difference.
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Citations
Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine–Gordon equation with damping
TL;DR: An efficient numerical scheme for solving the space fractional nonlinear damped sine-Gordon equation with periodic boundary condition based on the fast Fourier transform algorithm that is computationally efficient in long-time computations due to it does not involve matrix inversion.
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Fast dissipation-preserving difference scheme for nonlinear generalized wave equations with the integral fractional Laplacian
TL;DR: An efficient linearized iteration algorithm is exploited for the nonlinear system, such that it can be efficiently solved by the Krylov subspace solver with a suitable preconditioner, where the two-dimensional fast Fourier transform is used in the solver to accelerate the matrix-vector product.
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On τ-preconditioner for a novel fourth-order difference scheme of two-dimensional Riesz space-fractional diffusion equations
TL;DR: In this article , a τ-preconditioner for a novel fourth-order finite difference scheme of two-dimensional Riesz space-fractional diffusion equations (2D RSFDEs) is considered, in which a fourthorder fractional centered difference operator is adopted for the discretizations of spatial RIESz fractional derivatives, while the Crank-Nicolson method is adopted to discretize the temporal derivative.
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An energy-preserving computational approach for the semilinear space fractional damped Klein–Gordon equation with a generalized scalar potential
TL;DR: In this paper , a semi-implicit energy-preserving discrete numerical scheme for the Riesz space-fractional Klein-Gordon equation with a generalized scalar potential is constructed.
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A Nonlocal Fractional Peridynamic Diffusion Model
Yuanyuan Wang,HongGuang Sun,Siyuan Fan,Yan Gu,Xiangnan Yu +4 more
- 23 Jul 2021
TL;DR: In this paper, a non-local fractional peridynamic (FPD) model is proposed to characterize the non-locality of physical processes or systems, based on analysis with the fractional derivative model (FDM) and the per-idynamic model.
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