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The Grünwald-Letnikov method for fractional differential equations
This paper is devoted to the numerical treatment of fractional differential equations. Based on the Grunwald-Letnikov definition of fractional derivatives, finite difference schemes for theExpand
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Finite element method for two-dimensional space-fractional advection-dispersion equations
The backward Euler and Crank-Nicolson-Galerkin fully-discrete approximate schemes for two-dimensional space-fractional advection-dispersion equations are established. Firstly, we prove that theExpand
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Symplectic and multi-symplectic methods for the nonlinear Schrodinger equation
The Hamiltonian and the multi-symplectic formulations of the nonlinear Schrodinger equation are considered. For the multi-symplectic formulation, a new six-point difference scheme which is equivalentExpand
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Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations
Abstract In this article, a class of two-dimensional Riesz space fractional diffusion equations is considered. Some fractional spaces are established and some equivalences between fractionalExpand
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Convergence Analysis of a Block-by-block Method for Fractional Differential Equations
The block-by-block method, proposed by Linz for a kind of Volterra integral equations with nonsingular kernels, and extended by Kumar and Agrawal to a class of initial value problems of fractionalExpand
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  • Open Access
Mixed Finite Element Method for 2D Vector Maxwell's Eigenvalue Problem in Anisotropic Media
It is well known that the conventional edge element method in solving vector Maxwell's eigenvalue problem will lead to the presence of nonphysical zero eigenvalues. This paper uses the mixed flniteExpand
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  • Open Access
Finite difference/finite element method for two-dimensional space and time fractional Bloch-Torrey equations
In this paper, a class of two-dimensional space and time fractional Bloch-Torrey equations (2D-STFBTEs) are considered. Some definitions and properties of fractional derivative spaces are presented.Expand
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Finite element multigrid method for multi-term time fractional advection diffusion equations
In this paper, a class of multi-term time fractional advection diffusion equations (MTFADEs) is considered. By finite difference method in temporal direction and finite element method in spatialExpand
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  • Open Access
Symplectic wavelet collocation method for Hamiltonian wave equations
This paper introduces a novel symplectic wavelet collocation method for solving nonlinear Hamiltonian wave equations. Based on the autocorrelation functions of Daubechies compactly supported scalingExpand
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Spherical aberration effects in lens-axicon doublets: theoretical study.
Effects of spherical aberrations in converging and diverging lens-axicon doublets are investigated. Intensity profiles are obtained in the line and ring focal regions by numerically solving theExpand
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