An Optimal-Order Numerical Approximation to Variable-order Space-fractional Diffusion Equations on Uniform or Graded Meshes

DOI10.1137/19M1245621zbMath1429.65168WikidataQ126345394 ScholiaQ126345394MaRDI QIDQ5210548

Hong Wang, Xiangcheng Zheng

Publication date: 21 January 2020

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

collocation methodboundary-value problemoptimal-order error estimatevariable-order space-fractional diffusion equationuniform and graded mesh

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Boundary value problems for PDEs with pseudodifferential operators (35S15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A second-order accurate numerical method for the two-dimensional fractional diffusion equation
• Variable order differential equations with piecewise constant order-function and diffusion with changing modes
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• On time-fractional diffusion equations with space-dependent variable order
• Variable order and distributed order fractional operators
• Front propagation in reaction-diffusion systems with anomalous diffusion
• New integral inequalities with weakly singular kernel for discontinuous functions and their applications to impulsive fractional differential systems
• A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• Weakly Singular Discrete Gronwall Inequalities
• Regularity of the solution to 1-D fractional order diffusion equations
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Inhomogeneous Dirichlet Boundary-Value Problems of Space-Fractional Diffusion Equations and their Finite Element Approximations
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Variational formulation for the stationary fractional advection dispersion equation
• Variational formulation of problems involving fractional order differential operators
• Stochastic models for fractional calculus