Local discontinuous Galerkin method for distributed-order time and space-fractional convection-diffusion and Schrödinger type equations

2017/08/16 by Aboelenen, Tarek
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1708.05351

Abstract

Fractional partial differential equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we propose a local discontinuous Galerkin (LDG) method for the distributed-order time and Riesz space fractional convection-diffusion and Schrödinger type equations. We prove stability and optimal order of convergence O(h^N+1+(Δt)^1+\fracθ2+θ²) for the distributed-order time and space-fractional diffusion and Schrödinger type equations, an order of convergence of O(h^N+(1)/(2)+(Δt)^1+\fracθ2+θ²) is established for the distributed-order time and Riesz space fractional convection-diffusion equations where Δt, h and θ are the step sizes in time, space and distributed-order variables, respectively. Finally, the performed numerical experiments confirm the optimal order of convergence.

Related

• A direct discontinuous Galerkin method for fractional convection-diffusion and Schrödinger type equations
• Finite difference/local discontinuous Galerkin method for solving the fractional diffusion-wave equation
• Local discontinuous Galerkin method for the fractional diffusion equation with integral fractional Laplacian
• Local discontinuous Galerkin methods for the time tempered fractional diffusion equation
• Discontinuous Galerkin method for fractional convection-diffusion equations