NUMERICAL ANALYSIS OF AN IMPLICIT FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE FRACTIONAL ZAKHAROV–KUZNETSOV EQUATION

Numerical Analysis of the Fractional Seventh-order Kdv Equation Using an Implicit Fully Discrete Local Discontinuous Galerkin Method

In this paper an implicit fully discrete local discontinuous Galerkin (LDG) finite element method is applied to solve the time-fractional seventh-order Korteweg-de Vries (sKdV) equation, which is introduced by replacing the integer-order time derivatives with fractional derivatives. We prove that our scheme is unconditional stable and L error estimate for the linear case with the convergence ra...

A Fully Discrete Discontinuous Galerkin Method for Nonlinear Fractional Fokker-Planck Equation

The fractional Fokker-Planck equation is often used to characterize anomalous diffusion. In this paper, a fully discrete approximation for the nonlinear spatial fractional Fokker-Planck equation is given, where the discontinuous Galerkin finite element approach is utilized in time domain and the Galerkin finite element approach is utilized in spatial domain. The priori error estimate is derived...

An efficient fully-discrete local discontinuous Galerkin method for the Cahn-Hilliard-Hele-Shaw system

Nonlinear Cable equation, Fractional differential equation, Radial point interpolation method, Meshless local Petrov – Galerkin, Stability analysis

The cable equation is one the most fundamental mathematical models in the neuroscience, which describes the electro-diffusion of ions in denderits. New findings indicate that the standard cable equation is inadequate for describing the process of electro-diffusion of ions. So, recently, the cable model has been modified based on the theory of fractional calculus. In this paper, the two dimensio...

Local Discontinuous Galerkin Method for the Stochastic Heat Equation

In this paper we study the Local Discontinuous Galerkin scheme for solving the stochastic heat equation driven by the space white noise. We begin by giving a brief introduction to stochastic processes, stochastic differential equations, and their importance in the modern mathematical context. From there, using an example stochastic elliptic partial differential equation, we approximate the whit...