Solving a non-linear fractional convection-diffusion equation using local discontinuous Galerkin method

DOI10.1016/j.apnum.2021.02.003zbMath1475.65130OpenAlexW3126540277MaRDI QIDQ2029107

Hamid Safdari, Majid Rajabzadeh, Moein Khalighi

Publication date: 3 June 2021

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2021.02.003

zbMATH Keywords

fractional derivativesconvection-diffusion equationlocal discontinuous Galerkin method

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Fractional derivatives and integrals (26A33) Mittag-Leffler functions and generalizations (33E12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Integral equations with kernels of Cauchy type (45E05) Fractional partial differential equations (35R11) Numerical radial basis function approximation (65D12)

Related Items (3)

LDG approximation of a nonlinear fractional convection-diffusion equation using B-spline basis functions ⋮ Barycentric interpolation collocation algorithm to solve fractional differential equations ⋮ Spectral solutions for a class of nonlinear wave equations with Riesz fractional based on Legendre collocation technique

Cites Work

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• A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients
• Entropy formulation for fractal conservation laws
• Nonlinear fractional optimal control problems with neural network and dynamic optimization schemes
• A review of definitions for fractional derivatives and integral
• The \(\psi\)-Hilfer fractional calculus of variable order and its applications
• Hilfer-Katugampola fractional derivatives
• A Caputo fractional derivative of a function with respect to another function
• Computational algorithm for solving Fredholm time-fractional partial integrodifferential equations of Dirichlet functions type with error estimates
• The local discontinuous Galerkin method for convection-diffusion-fractional anti-diffusion equations
• Leibniz type rule: \(\psi\)-Hilfer fractional operator
• On the \(\psi\)-Hilfer fractional derivative
• A new collection of real world applications of fractional calculus in science and engineering
• Riesz fractional derivatives and fractional dimensional space
• Modeling some real phenomena by fractional differential equations
• A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems
• The discontinuous Galerkin method for fractal conservation laws
• OCCURRENCE AND NON-APPEARANCE OF SHOCKS IN FRACTAL BURGERS EQUATIONS
• A numerical method for fractal conservation laws
• Solving fractional optimal control problems with fixed or free final states by Haar wavelet collocation method
• An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative
• Local Discontinuous Galerkin methods for fractional diffusion equations
• Fractional Calculus
• Discontinuous Galerkin Method for Fractional Convection-Diffusion Equations

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