Convergence analysis of the space fractional-order diffusion equation based on the compact finite difference scheme

DOI10.1007/s40314-020-1078-zzbMath1463.65244OpenAlexW3005998612MaRDI QIDQ2176208

Yanyan Li

Publication date: 4 May 2020

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-020-1078-z

zbMATH Keywords

stabilityconvergenceChebyshev collocation methodcompact finite differencespace fractional-order diffusion equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Best approximation, Chebyshev systems (41A50) 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) Financial applications of other theories (91G80) Free boundary problems for PDEs (35R35) Fractional partial differential equations (35R11) Functional-differential equations with fractional derivatives (34K37) Interpolation and approximation (educational aspects) (97N50)

Related Items (21)

Improving split-step forward methods by ODE solver for stiff stochastic differential equations ⋮ THE NUMERICAL STRATEGY OF TEMPERED FRACTIONAL DERIVATIVE IN EUROPEAN DOUBLE BARRIER OPTION ⋮ Nonlinear dynamics of the Burgers' equation and numerical experiments ⋮ Analysis of fractional-order population model of diabetes and effect of remission through lifestyle intervention ⋮ An approximate method based on Bernstein polynomials for solving fractional PDEs with proportional delays ⋮ Meshfree methods for nonlinear equilibrium radiation diffusion equation with jump coefficient ⋮ A fast preconditioning iterative method for solving the discretized second-order space-fractional advection-diffusion equations ⋮ A novel numerical manner for two‐dimensional space fractional diffusion equation arising in transport phenomena ⋮ A CONVERGENCE ANALYSIS OF THE MOBILE–IMMOBILE ADVECTION–DISPERSION MODEL OF TEMPORAL FRACTIONAL ORDER ARISING IN WATERSHED CATCHMENTS AND RIVERS ⋮ Pell-Lucas discretization method for finding the solution of Caputo-Fabrizio time-fractional diffusion equations ⋮ Mean-square convergence analysis of the semi-implicit scheme for stochastic differential equations driven by the Wiener processes ⋮ Reproducing kernel method to solve non-local fractional boundary value problem ⋮ Unnamed Item ⋮ A tau method based on Jacobi operational matrix for solving fractional telegraph equation with Riesz-space derivative ⋮ Unnamed Item ⋮ The impact of Chebyshev collocation method on solutions of fractional advection-diffusion equation ⋮ Numerical treatment of the space fractional advection-dispersion model arising in groundwater hydrology ⋮ Numerical treatment for Burgers-Fisher and generalized Burgers-Fisher equations ⋮ The impact of the Chebyshev collocation method on solutions of the time-fractional Black-Scholes ⋮ Numerical investigation of the two-dimensional space-time fractional diffusion equation in porous media ⋮ Numerical simulation to solve two-dimensional temporal-space fractional Bloch-Torrey equation taken of the spin magnetic moment diffusion

Cites Work

• Unnamed Item
• Unnamed Item
• Numerical approximations for fractional diffusion equations via splines
• A tau approach for solution of the space fractional diffusion equation
• Homotopy analysis method for fractional IVPs
• On the numerical solutions for the fractional diffusion equation
• Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation
• The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method
• Chebyshev polynomials of the second, third and fourth kinds in approximation, indefinite integration, and integral transforms
• An accurate and cost-efficient numerical approach to analyze the initial and boundary value problems of fractional multi-order
• Numerical investigation of the time fractional mobile-immobile advection-dispersion model arising from solute transport in porous media
• Approximate analytical solution for seepage flow with fractional derivatives in porous media
• Finite difference approximations for fractional advection-dispersion flow equations
• A computationally efficient method for tempered fractional differential equations with application
• Numerical investigation of the nonlinear modified anomalous diffusion process
• Shifted fractional Jacobi spectral algorithm for solving distributed order time-fractional reaction-diffusion equations
• A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains
• A high-order compact difference method for time fractional Fokker-Planck equations with variable coefficients
• A fast finite-difference algorithm for solving space-fractional filtration equation with a generalised Caputo derivative
• Numerical analysis of time fractional Black-Scholes European option pricing model arising in financial market
• A second-order accurate numerical approximation for the fractional diffusion equation
• Existence of Turing Instabilities in a Two-Species Fractional Reaction-Diffusion System
• Numerical Approximation of a Time Dependent, Nonlinear, Space‐Fractional Diffusion Equation
• Spectral Methods
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: Convergence analysis of the space fractional-order diffusion equation based on the compact finite difference scheme