A Finite Difference Method for Space Fractional Differential Equations with Variable Diffusivity Coefficient
作者机构：Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahran 31261Kingdom of Saudi Arabia ComputerElectricalMathermatical Sciences and Engineering DivisionKing Abdullah University of Science and TechnologyThuwal 23955Kingdom of Saudi Arabia CNRSLIMSIUniversitéParis-SaclayCampus Universitaire-BP 13391403 OrsayFrance
出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)
年 卷 期：2020年第2卷第4期
页 面：671-688页
核心收录：
学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学]
基 金：The support of the King Fahd University of Petroleum and Minerals(KFUPM)through the project No.KAUST0O5 is gratefully acknowledged Research reported in this publication was also sup-ported by the research funding from the King Abdullah University of Science and Technology(KAUST)
主 题：Two-sided fractional derivatives Variable coefcients Finite diferences
摘 要：Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations,but is better described by fractional diffusion *** nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathemati-cal analysis of these models and the establishment of suitable numerical *** paper proposes and analyzes the first finite difference method for solving variable-coefficient one-dimensional(steady state)fractional differential equations(DEs)with two-sided fractional derivatives(FDs).The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided FD when the right-sided FD is approximated by two consecutive applications of the first-order backward Euler *** scheme reduces to the standard second-order central difference in the absence of *** existence and uniqueness of the numerical solution are proved,and truncation errors of order h are demonstrated(h denotes the maximum space step size).The numerical tests illustrate the global 0(h)accu-racy,except for nonsmooth cases which,as expected,have deteriorated convergence rates.
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