一类奇异摄动Fredholm型积分微分方程的二阶自适应移动网格方法  

The Second Order Adaptive Moving Mesh Method for a Singularly Perturbed Fredholm Integro-Differential Equation

作　　者：罗丹 毛志 LUO Dan;MAO Zhi(School of Mathematics and Statistics,Jishou University,Jishou 416100,Hunan China;School of Data Science,Tongren University,Tongren 554300,Guizhou China)

机构地区：[1]吉首大学数学与统计学院,湖南吉首416000 [2]铜仁学院大数据学院,贵州铜仁554300

出　　处：《吉首大学学报（自然科学版）》2024年第4期15-25,共11页Journal of Jishou University(Natural Sciences Edition)

基　　金：贵州省第六届高层人才创新项目(2022(2020)040)。

摘　　要：利用基函数方法和复合梯形公式构建了指数拟合有限差分格式,用该有限差分格式对一类奇异摄动Fredholm型积分微分方程进行了离散.用推导出的数值解的截断误差估计,并结合边界估计和稳定性分析,证明了自适应移动网格方法关于摄动参数在无穷范数意义下具有二阶一致收敛性.在理论分析的基础上,设计出二阶自适应移动网格生成算法.An exponentially fitted finite difference scheme constructed by the base function method and the compound trapezoidal formula is applied to make discrete a class of singularly perturbed Fredholm integral differential equation.Combining the truncation error estimate,the boundary estimate and the stability analysis,the second order uniform convergence in the infinity norm with respect to the perturbation parameter for the adaptive moving mesh method is proved.Based on the above theoretical analysis,the algorithm to produce the mesh is designed.

关 键 词：奇异摄动 Fredholm型积分方程 自适应移动网格 一致收敛 

分 类 号：O241.8[理学—计算数学]