A fourth-order compact solution of the two-dimensional modified anomalous fractional sub-diffusion equation with a nonlinear source term

DOI10.1016/j.camwa.2013.08.010zbMath1350.65083OpenAlexW2042993252MaRDI QIDQ316143

Mostafa Abbaszadeh, Akbar Mohebbi

Publication date: 26 September 2016

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2013.08.010

zbMATH Keywords

convergencenumerical resultsFourier analysisunconditional stabilitytwo-dimensionalcompact finite differenceGrünwald-Letnikov discretizationmodified anomalous sub-diffusionRiemann-Liouville derivatives

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) 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)

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Cites Work

• Unnamed Item
• The sinc-Legendre collocation method for a class of fractional convection-diffusion equations with variable coefficients
• A compact difference scheme for the fractional diffusion-wave equation
• A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations
• Finite element approximation for a modified anomalous subdiffusion equation
• A tau approach for solution of the space fractional diffusion equation
• Compact finite difference method for the fractional diffusion equation
• Finite difference approximations for the fractional Fokker-Planck equation
• A new operational matrix for solving fractional-order differential equations
• Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
• The use of compact boundary value method for the solution of two-dimensional Schrödinger equation
• Computational algorithms for computing the fractional derivatives of functions
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Numerical solution of the space fractional Fokker-Planck equation.
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• Numerical analysis of the Rayleigh-Stokes problem for a heated generalized second-grade fluid with fractional derivatives
• Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term
• Compact finite difference scheme for the solution of time fractional advection-dispersion equation
• A high-order and unconditionally stable scheme for the modified anomalous fractional sub-diffusion equation with a nonlinear source term
• A Fourier method for the fractional diffusion equation describing sub-diffusion
• Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation
• A second-order accurate numerical approximation for the fractional diffusion equation
• A fully discrete difference scheme for a diffusion-wave system
• Weighted average finite difference methods for fractional diffusion equations
• A Legendre collocation method for fractional integro-differential equations
• New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• The fractional diffusion equation
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Solving nonlinear fractional partial differential equations using the homotopy analysis method
• From diffusion to anomalous diffusion: A century after Einstein’s Brownian motion
• Analysis of fractional differential equations