Superconvergence and postprocessing of collocation methods for fractional differential equations

DOI10.1007/s10915-023-02339-7zbMath1530.65187OpenAlexW4386891445MaRDI QIDQ6077296

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Publication date: 17 October 2023

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-023-02339-7

zbMATH Keywords

collocation methodssuperconvergencefractional differential equationsVolterra integral equationsinterpolation postprocessing

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Volterra integral equations (45D05) Fractional ordinary differential equations (34A08)

Cites Work

• A new difference scheme for the time fractional diffusion equation
• A multi-domain spectral method for time-fractional differential equations
• The Galerkin finite element method for a multi-term time-fractional diffusion equation
• An efficient collocation method for a Caputo two-point boundary value problem
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Collocation methods for general Caputo two-point boundary value problems
• Detailed error analysis for a fractional Adams method
• Superconvergence of interpolated collocation solutions for weakly singular Volterra integral equations of the second kind
• A posteriori error analysis for variable-coefficient multiterm time-fractional subdiffusion equations
• Fast conservative numerical algorithm for the coupled fractional Klein-Gordon-Schrödinger equation
• Numerical solution of nonlinear fractional differential equations by spline collocation methods
• A high order schema for the numerical solution of the fractional ordinary differential equations
• A fully discrete difference scheme for a diffusion-wave system
• Mittag-Leffler stability of numerical solutions to time fractional ODEs
• Fractional boundary value problems: Analysis and numerical methods
• Volterra Integral Equations
• Numerical Algorithms for Time-Fractional Subdiffusion Equation with Second-Order Accuracy
• The Numerical Solution of Weakly Singular Volterra Integral Equations by Collocation on Graded Meshes
• The Numerical Solution of Integral Equations of the Second Kind
• Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers
• Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• TWO COLLOCATION TYPE METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-LOCAL BOUNDARY CONDITIONS
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
• An Optimal-Order Numerical Approximation to Variable-order Space-fractional Diffusion Equations on Uniform or Graded Meshes
• The Convergence of Collocation Solutions in Continuous Piecewise Polynomial Spaces for Weakly Singular Volterra Integral Equations
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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