A monotone finite volume method for time fractional Fokker-Planck equations  

作　　者：Yingjun Jiang Xuejun Xu 

机构地区：[1]School of Mathematics and Statistics, Changsha University of Science and Technology [2]Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science, Chinese Academy of Sciences [3]School of Mathematical Sciences, Tongji University

出　　处：《Science China Mathematics》2019年第4期783-794,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11571053, 11671302, 51239001 and 91647118)

摘　　要：We develop a monotone finite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is of order 1 in the space and if the space grid becomes sufficiently fine, the convergence rate can be improved to order 2.Numerical results are given to support our theoretical findings. One characteristic of our method is that it has monotone property such that it keeps the nonnegativity of some physical variables such as density, concentration,etc.We develop a monotone ?nite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is of order 1 in the space and if the space grid becomes suffciently ?ne, the convergence rate can be improved to order 2.Numerical results are given to support our theoretical ?ndings. One characteristic of our method is that it has monotone property such that it keeps the nonnegativity of some physical variables such as density, concentration,etc.

关 键 词：time FRACTIONAL FOKKER-PLANCK EQUATIONS FINITE volume methods MONOTONE CONVERGENCE 

分 类 号：O1[理学—数学]