Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions (Q2310114)

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English	Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions	scientific article

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instance of

scholarly article

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title

Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions (English)

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zbMATH Open document ID

1439.65081

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DOI

10.1016/j.cma.2017.08.029

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author

Fanhai Zeng

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Zhongqiang Zhang

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George Em. Karniadakis

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published in

Computer Methods in Applied Mechanics and Engineering

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publication date

6 April 2020

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full work available at URL

https://arxiv.org/abs/1701.00996

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Mathematics Subject Classification ID

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FODEs

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time-fractional diffusion-wave equation

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shifted Grünwald-Letnikov formula

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low regularity

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MaRDI profile type

MaRDI publication profile

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The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type

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Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

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Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation

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Q4233638

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A Fourier method for the fractional diffusion equation describing sub-diffusion

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Stability and convergence of finite difference schemes for a class of time-fractional sub-diffusion equations based on certain superconvergence

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Finite difference approximations for fractional advection-dispersion flow equations

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Finite difference/spectral approximations for the time-fractional diffusion equation

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Finite difference methods for the time fractional diffusion equation on non-uniform meshes

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A class of second order difference approximations for solving space fractional diffusion equations

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Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation

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Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative

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High-order algorithms for Riesz derivative and their applications. I.

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High-order algorithms for Riesz derivative and their applications. II

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A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation

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Convolution quadrature time discretization of fractional diffusion-wave equations

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Discretized Fractional Calculus

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Weighted average finite difference methods for fractional diffusion equations

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Second-order stable finite difference schemes for the time-fractional diffusion-wave equation

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The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation

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Numerical Algorithms for Time-Fractional Subdiffusion Equation with Second-Order Accuracy

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Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations

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Fractional Spectral Collocation Method

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A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations

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A high-order spectral method for the multi-term time-fractional diffusion equations

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Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations

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Nonpolynomial collocation approximation of solutions to fractional differential equations

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Superconvergence of a Discontinuous Galerkin Method for Fractional Diffusion and Wave Equations

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HOW TO APPROXIMATE THE FRACTIONAL DERIVATIVE OF ORDER 1 < α ≤ 2

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Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

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Numerical methods for solving the multi-term time-fractional wave-diffusion equation

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Efficient and Stable Numerical Methods for Multi-Term Time Fractional Sub-Diffusion Equations

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The Galerkin finite element method for a multi-term time-fractional diffusion equation

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Maximum principle and numerical method for the multi-term time-space Riesz-Caputo fractional differential equations

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Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

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Spline collocation methods for linear multi-term fractional differential equations

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A Finite Element Method with Singularity Reconstruction for Fractional Boundary Value Problems

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Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients

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A high-accuracy preserving spectral Galerkin method for the Dirichlet boundary-value problem of variable-coefficient conservative fractional diffusion equations

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Optimal Error Estimates of Spectral Petrov--Galerkin and Collocation Methods for Initial Value Problems of Fractional Differential Equations

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A second-order accurate numerical method for a fractional wave equation

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A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels

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Generalized Jacobi functions and their applications to fractional differential equations

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Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials

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Quasi-compact finite difference schemes for space fractional diffusion equations

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Detailed error analysis for a fractional Adams method

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Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

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Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients

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Pitfalls in fast numerical solvers for fractional differential equations

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A Stability Analysis of Convolution Quadraturea for Abel-Volterra Integral Equations

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The Finite Difference Methods for Fractional Ordinary Differential Equations

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Q4303980

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Spectral Methods

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mardi Publication:2310114