Semi-discretized numerical solution for time fractional convection-diffusion equation by RBF-FD

DOI10.1016/j.aml.2021.107880OpenAlexW4200097900MaRDI QIDQ2077078

Yanyan Li

Publication date: 22 February 2022

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

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107880

zbMATH Keywords

finite differenceradial basis functionCaputo derivativemultiquadrictime fractional convection-diffusion equation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Fractional partial differential equations (35R11)

Related Items

Trajectories and singular points of two-dimensional fractional-order autonomous systems, Existence and uniqueness of weak solutions to a truncated system for a class of time-fractional reaction-diffusion-advection systems, Iterative optimization method for determining optimal shape parameter in RBF-FD method, Spectral solutions for a class of nonlinear wave equations with Riesz fractional based on Legendre collocation technique

Uses Software

• FODE

Cites Work

• Unnamed Item
• A meshless method to the solution of an ill-posed problem
• Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations
• An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
• An implicit RBF meshless approach for time fractional diffusion equations
• High-order finite element methods for time-fractional partial differential equations
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• RBF-FD formulas and convergence properties
• Stabilization of RBF-generated finite difference methods for convective PDEs
• Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion
• On using radial basis functions in a ``finite difference mode with applications to elasticity problems
• A new operational matrix for solving fractional-order differential equations
• The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems
• A novel space-time meshless method for nonhomogeneous convection-diffusion equations with variable coefficients
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Finite difference approximations for fractional advection-dispersion flow equations
• Error estimates and condition numbers for radial basis function interpolation
• Numerical solution of fractional advection-diffusion equation with a nonlinear source term
• Fourth order compact FD methods for convection diffusion equations with variable coefficients
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Fractional Green function for linear time-fractional inhomogeneous partial differential equations in fluid mechanics
• A PDE Approach to Space-Time Fractional Parabolic Problems
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• Local RBF-FD solutions for steady convection–diffusion problems
• Finite Element Method for the Space and Time Fractional Fokker–Planck Equation