A Petrov-Galerkin spectral method for fractional convection–diffusion equations with two-sided fractional derivative

DOI10.1080/00207160.2020.1759802zbMath1480.65356OpenAlexW3026321595MaRDI QIDQ5031249

Wenting Mao, Yunqing Huang, Yanping Chen, Huasheng Wang

Publication date: 18 February 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2020.1759802

zbMATH Keywords

error estimatesboundary value problemfractional convection-diffusion equationsPetrov-Galerkin spectral methodtwo-sided fractional derivative

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12)

Uses Software

• FODE

Cites Work

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• Fractional Sturm-Liouville eigen-problems: theory and numerical approximation
• Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations
• A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients
• Numerical analysis of fully discretized Crank-Nicolson scheme for fractional-in-space Allen-Cahn equations
• An \(h\)-\(p\) version of the continuous Petrov-Galerkin finite element method for Riemann-Liouville fractional differential equation with novel test basis functions
• Integral representations for Jacobi polynomials and some applications
• A Petrov--Galerkin Finite Element Method for Fractional Convection-Diffusion Equations
• Generalized Jacobi functions and their applications to fractional differential equations
• A PDE Approach to Space-Time Fractional Parabolic Problems
• Optimal Fractional Integration Preconditioning and Error Analysis of Fractional Collocation Method Using Nodal Generalized Jacobi Functions
• Wellposedness of Variable-Coefficient Conservative Fractional Elliptic Differential Equations
• A Generalized Spectral Collocation Method with Tunable Accuracy for Fractional Differential Equations with End-Point Singularities
• Numerical Algorithms for Time-Fractional Subdiffusion Equation with Second-Order Accuracy
• A Space-Time Spectral Method for the Time Fractional Diffusion Equation
• A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
• Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
• Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
• Stochastic models for fractional calculus

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