Error analysis of the Legendre-Gauss collocation methods for the nonlinear distributed-order fractional differential equation

DOI10.1016/j.apnum.2019.03.005zbMath1450.65134OpenAlexW2923915969WikidataQ115360406 ScholiaQ115360406MaRDI QIDQ2311789

Yanming Zhang, Jingjun Zhao, Yang Xu

Publication date: 4 July 2019

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2019.03.005

zbMATH Keywords

convergenceLegendre-Gauss collocation methoddistributed-order fractional differential equation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical quadrature and cubature formulas (65D32) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Classical solutions to PDEs (35A09)

Related Items (9)

The construction of a new operational matrix of the distributed-order fractional derivative using Chebyshev polynomials and its applications ⋮ Shifted Legendre polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model ⋮ High-order numerical method for solving a space distributed-order time-fractional diffusion equation ⋮ Shifted Bernstein-Legendre polynomial collocation algorithm for numerical analysis of viscoelastic Euler-Bernoulli beam with variable order fractional model ⋮ Wavelet approximation scheme for distributed order fractional differential equations ⋮ Polynomial-Sinc collocation method combined with the Legendre-Gauss quadrature rule for numerical solution of distributed order fractional differential equations ⋮ Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations ⋮ A generalized Legendre-Gauss collocation method for solving nonlinear fractional differential equations with time varying delays ⋮ A new operational matrix based on Müntz-Legendre polynomials for solving distributed order fractional differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical solution of distributed order fractional differential equations
• Numerical approximation of distributed order reaction-diffusion equations
• Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method
• Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
• Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
• A new Jacobi operational matrix: an application for solving fractional differential equations
• A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations
• The mean value theorem and analytic functions of a complex variable
• On a nonlinear distributed order fractional differential equation
• Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation
• A new operational matrix for solving fractional-order differential equations
• Numerical analysis for distributed-order differential equations
• Legendre-Gauss collocation methods for ordinary differential equations
• Convolution quadrature and discretized operational calculus. I
• An efficient technique based on finite difference/finite element method for solution of two-dimensional space/multi-time fractional Bloch-Torrey equations
• Variable order and distributed order fractional operators
• On the numerical inversion of the Laplace transform of certain holomorphic mappings
• A generalized model for the uniaxial isothermal deformation of a viscoelastic body
• Two alternating direction implicit difference schemes with the extrapolation method for the two-dimensional distributed-order differential equations
• A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation
• Spectral element technique for nonlinear fractional evolution equation, stability and convergence analysis
• Some high-order difference schemes for the distributed-order differential equations
• Finite difference/spectral approximations for the distributed order time fractional reaction-diffusion equation on an unbounded domain
• Spectral Methods
• Distributed-Order Dynamic Systems
• Runge-Kutta Theory for Volterra and Abel Integral Equations of the Second Kind
• Variational solution of fractional advection dispersion equations on bounded domains in ℝd
• A Spectral Order Method for Inverting Sectorial Laplace Transforms
• A Space-Time Spectral Method for the Time Fractional Diffusion Equation
• Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel
• Stability and Euler Approximation of One-sided Lipschitz Differential Inclusions
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Solving nonlinear fractional partial differential equations using the homotopy analysis method
• Petrov--Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations
• Fast and Oblivious Convolution Quadrature
• The dual reciprocity boundary integral equation technique to solve a class of the linear and nonlinear fractional partial differential equations
• Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

This page was built for publication: Error analysis of the Legendre-Gauss collocation methods for the nonlinear distributed-order fractional differential equation