High-order Numerical Methods for Riesz Space Fractional Turbulent Diffusion Equation

Abstract

Numerical methods for fractional calculus attract increasing interests due to its wide applications in various fields such as physics, mechanics, etc. In this paper, we focus on constructing high-order algorithms for Riesz derivatives, where the convergence orders cover from the second order to the sixth order. Then we apply the established schemes to the Riesz space fractional turbulent diffusion equation. Numerical experiments are displayed which support the theoretical analysis.

References in corpus (5)

• A new difference scheme for the time fractional diffusion equation
• High-order Numerical Methods for Riesz Space Fractional Turbulent Diffusion Equation
• Numerical Approximations for Fractional Differential Equations
• Numerical solution of fractional Sturm-Liouville equation in integral form
• Analytic solutions of fractional differential equations by operational methods

Cited by in corpus (6)

• High-order Numerical Methods for Riesz Space Fractional Turbulent Diffusion Equation
• Approximations for the Caputo derivative (II)
• Higher-Order Numerical Solutions of the Fractional Relaxation-Oscillation Equation using Fractional Integration
• Second order difference approximation for a class of Riesz space fractional advection-dispersion equations with delay
• Asymptotic expansions and approximations for the Caputo derivative
• Fractional-compact numerical algorithms for Riesz spatial fractional reaction-dispersion equations