非线性偏积分微分方程紧隐显BDF方法的误差分析  

Error Analysis of Compact Implicit-Explicit BDF Method for Nonlinear Partial Integral Differential Equations

作　　者：兰海峰 肖飞雁 张根根 朱瑞 LAN Haifeng;XIAO Feiyan;ZHANG Gengen;ZHU Rui(College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541006

出　　处：《广西师范大学学报（自然科学版）》2020年第4期82-91,共10页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11701110);广西学位与研究生教育改革课题(JGY2017019);广西研究生教育创新计划(YCSW2019087)。

摘　　要：本文研究一类非线性抛物型偏积分微分方程数值格式的误差分析,其格式在空间方向采用紧致差分方法,时间方向采用隐显BDF方法,积分项利用梯形数值求积公式进行求解,给出了算法的收敛阶O(τ^2+h^4);通过数值算例验证了数值格式的准确性和有效性。In this paper,the compact implicit-explicit BDF method are proposed to solve nonlinear partial integral differential equations,i.e.the equation is discretized by the implicit-explicit BDF method in time and compact finite difference approximations in space.Then,the global convergence of the scheme is proved rigorously with convergence order O(τ^2+h^4).Finally,numerical examples are presented to verify the accuracy and validity of the numerical scheme.

关 键 词：非线性偏积分微分方程 隐显BDF方法 紧致差分方法 误差分析 

分 类 号：O241.82[理学—计算数学]