广西师范大学学报（自然科学版） ›› 2020, Vol. 38 ›› Issue (4): 82-91.doi: 10.16088/j.issn.1001-6600.2020.04.010

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非线性偏积分微分方程紧隐显BDF方法的误差分析

兰海峰, 肖飞雁*, 张根根, 朱瑞   

  1. 广西师范大学数学与统计学院, 广西桂林541006
  • 收稿日期:2019-03-25 发布日期:2020-07-13
  • 通讯作者: 肖飞雁(1973—), 女(土家族), 广西师范大学教授, 博士。E-mail: fyxiao@mailbox.gxnu.edu.cn
  • 基金资助:
    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)

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

LAN Haifeng, XIAO Feiyan*, ZHANG Gengen, ZHU Rui   

  1. College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2019-03-25 Published:2020-07-13

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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(τ2+h4);通过数值算例验证了数值格式的准确性和有效性。

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

Abstract: 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(τ2+h4). Finally, numerical examples are presented to verify the accuracy and validity of the numerical scheme.

Key words: nonlinear partial integro-differential equation, implicit-explicit BDF, compact difference scheme, error analysis

中图分类号: 

  • O241.82
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