A kind of product integration scheme for solving fractional ordinary differential equations

DOI10.1016/j.apnum.2018.10.014zbMath1405.65180OpenAlexW2899845772MaRDI QIDQ1633331

Jingjun Zhao, Yang Xu, Yu Li

Publication date: 19 December 2018

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.10.014

zbMATH Keywords

product integrationCaputo fractional derivativefractional differential equationlocal Fourier expansion

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Volterra integral equations (45D05) Fractional ordinary differential equations (34A08)

Related Items (5)

Numerical analysis of block-by-block method for a class of fractional relaxation-oscillation equations ⋮ A collocation methods based on the quadratic quadrature technique for fractional differential equations ⋮ A new numerical method for solving semilinear fractional differential equation ⋮ A kind of generalized backward differentiation formulae for solving fractional differential equations ⋮ Generalized Mittag-Leffler quadrature methods for fractional differential equations

Cites Work

• Unnamed Item
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• Exponentially accurate spectral and spectral element methods for fractional ODEs
• Higher order numerical methods for solving fractional differential equations
• A simple framework for the derivation and analysis of effective one-step methods for ODEs
• Jacobian-predictor-corrector approach for fractional differential equations
• Numerical approaches to fractional calculus and fractional ordinary differential equation
• On accurate product integration rules for linear fractional differential equations
• Recent history of fractional calculus
• Local discontinuous Galerkin methods for fractional ordinary differential equations
• A product integration approach based on new orthogonal polynomials for nonlinear weakly singular integral equations
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Stability results for collocation methods for Volterra integral equations
• A new approach to the numerical solution of weakly singular Volterra integral equations.
• Detailed error analysis for a fractional Adams method
• A predictor-corrector approach for the numerical solution of fractional differential equations
• Trapezoidal methods for fractional differential equations: theoretical and computational aspects
• Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
• A high order schema for the numerical solution of the fractional ordinary differential equations
• Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
• Stability of collocation for weakly singular Volterra equations
• Product integration for Volterra integral equations of the second kind with weakly singular kernels
• The Finite Difference Methods for Fractional Ordinary Differential Equations
• Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation
• Time-Splitting Schemes for Fractional Differential Equations I: Smooth Solutions
• Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems

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