Abstract
In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. We show that our scheme is unconditional stable and L 2 error estimate for the linear case with the convergence rate through analysis.
Highlights
During the last few decades the numerical modeling and simulation for fractional calculus have been the focus of many studies, and various fractional order differential equation have been solved including e.g. space-time fractional partial differential equation [10], space and time fractional Fokker–Planck equation [5], fractional order two point boundary value problem [7], the fractional Korteweg–de Vries (KdV) equation [13], fractional convection-diffusion equation [14], fractional partial differential equations fluid mechanics [15], fractional KdV–Burgers–Kuramoto equation [16] and so on
Stability is ensured by a careful choice of interface numerical fluxes
We prove that our scheme is unconditionally stable and L2 error estimate for the linear case with the convergence rate
Summary
During the last few decades the numerical modeling and simulation for fractional calculus have been the focus of many studies, and various fractional order differential equation have been solved including e.g. space-time fractional partial differential equation [10], space and time fractional Fokker–Planck equation [5], fractional order two point boundary value problem [7], the fractional KdV equation [13], fractional convection-diffusion equation [14], fractional partial differential equations fluid mechanics [15], fractional KdV–Burgers–Kuramoto equation [16] and so on.
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