求解具有非线性源项的双侧空间分数阶扩散方程的样条方法  

Spline approach for the two-side space fractional diffusion equation with a nonlinear source term

作　　者：陈雪娟[1] 陈景华[1,2] 章红梅[3] CHEN Xuejuan;CHEN Jinghua;ZHANG Hongmei(School of Sciences,Jimei University,Xiamen 361021,China;Digital Fujian Big Data Modeling and Intelligent Computing Institute,Jimei University,Xiamen 361021,China;School of Mathematical and Computer Sciences,Fuzhou University,Fuzhou 350108,China)

机构地区：[1]集美大学理学院,福建厦门361021 [2]集美大学数字福建大数据建模与智能计算研究所,福建厦门361021 [3]福州大学数学与计算机科学学院,福建福州350108

出　　处：《厦门大学学报（自然科学版）》2021年第6期981-988,共8页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11801214);福建省自然科学基金(2020J01703);集美大学国家基金培育计划(ZP2020054);集美大学数字福建大数据建模与智能计算研究所开放基金。

摘　　要：基于多项式样条函数,提出一种求解具有非线性源项的双侧空间分数阶扩散方程的数值方法.通过傅里叶分析证明了所提出的数值方法是无条件稳定和收敛的.为了验证所构造差分格式的有效性,引入分数阶行方法(MOL)与之进行比较.最后给出数值例子,并验证数值结果与理论分析是相吻合的.In this paper,a numerical method based on the quadratic polynomial spline function is used to find the approximate solution for the two-side space fractional diffusion equation containing a nonlinear source term.The proposed method is proved to be unconditionally stable and convergent by Fourier analysis.For the purpose of evaluating the efficiency of the method,comparison with a fractional method of lines is made.Finally,some numerical examples are presented to show that numerical results agree satisfactorily with our theoretical analysis.

关 键 词：分数阶扩散方程 非线性源项 二次多项式样条函数 行方法 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]