New group iterative schemes in the numerical solution of the two-dimensional time fractional advection-diffusion equation

DOI10.1080/23311835.2017.1412241zbMath1427.65143OpenAlexW2775089783MaRDI QIDQ5193466

Alla Tareq Balasim, Norhashidah Hj. Mohd. Ali

Publication date: 10 September 2019

Published in: Cogent Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/23311835.2017.1412241

zbMATH Keywords

Caputo fractional derivativetwo-dimensional problemstability and convergence analysisgroup methodsCrank-Nicolson difference schemestime-fractional advection-diffusion

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) 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) Fractional partial differential equations (35R11)

Related Items

Efficient numerical simulations based on an explicit group approach for the time fractional advection-diffusion reaction equation, TRAVELING WAVE SOLUTIONS TO A MATHEMATICAL MODEL OF FRACTIONAL ORDER (2+1)-DIMENSIONAL BREAKING SOLITON EQUATION, An RBF-FD method for the time-fractional advection-dispersion equation with nonlinear source term, High-order rotated grid point iterative method for solving 2D time fractional telegraph equation and its convergence analysis, On rotated grid point iterative method for solving 2D fractional reaction–subdiffusion equation with Caputo–Fabrizio operator, Efficient hybrid group iterative methods in the solution of two-dimensional time fractional cable equation, A high-order numerical scheme based on graded mesh and its analysis for the two-dimensional time-fractional convection-diffusion equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A mathematical model for simulation of a water table profile between two parallel subsurface drains using fractional derivatives
• New explicit group iterative methods in the solution of three dimensional hyperbolic telegraph equations
• On Riemann-Liouville and Caputo derivatives
• A characteristic difference method for the transient fractional convection-diffusion equations
• Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term
• Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation
• RBFs approximation method for time fractional partial differential equations
• ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation
• A note on the finite element method for the space-fractional advection diffusion equation
• Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
• Modified implicit fractional difference scheme for 2D modified anomalous fractional sub-diffusion equation
• A new difference scheme for time fractional heat equations based on the Crank-Nicholson method
• A general finite element formulation for fractional variational problems
• Compact finite difference scheme for the solution of time fractional advection-dispersion equation
• Fractional Pearson diffusions
• New explicit group iterative methods in the solution of two dimensional hyperbolic equations
• A spectral Legendre-Gauss-Lobatto collocation method for a space-fractional advection diffusion equations with variable coefficients
• Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation
• A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative
• Superlinearly convergent algorithms for the two-dimensional space-time Caputo-Riesz fractional diffusion equation
• Finite element method for two-dimensional time-fractional tricomi-type equations
• Spectral approximations to the fractional integral and derivative
• Time-dependent fractional advection-diffusion equations by an implicit MLS meshless method
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• The fractional diffusion equation
• Explicit group iterative methods for solving elliptic partial differential equations in 3-space dimensions
• An efficient four points modified explicit group poisson solver
• EXPLICIT DE-COUPLED GROUP ITERATIVE METHODS AND THEIR PARALLEL IMPLEMENTATIONS
• Parallel block interface domain decomposition methods for the 2D convection–diffusion equation