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求解刚性Volterra延迟积分微分方程的隐显单支方法的稳定性与误差分析

张根根1,2, 唐蕾2, 肖爱国2   

  1. 1. 广西师范大学 数学与统计学院, 桂林 541004;
    2. 湘潭大学数学与计算科学学院, 湘潭 411105
  • 收稿日期:2016-12-31 出版日期:2018-03-15 发布日期:2018-02-03
  • 基金资助:

    国家自然科学基金项目(No.11671343,11271311,11701110),广西高等学校高水平创新团队及卓越学者计划资助.

张根根, 唐蕾, 肖爱国. 求解刚性Volterra延迟积分微分方程的隐显单支方法的稳定性与误差分析[J]. 计算数学, 2018, 40(1): 33-48.

Zhang Gengen, Tang Lei, Xiao Aiguo. STABILITY AND ERROR ANALYSIS OF IMPLICIT-EXPLICIT ONE-LEG METHODS FOR STIFF VOLTERRA DELAY INTEGRO-DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2018, 40(1): 33-48.

STABILITY AND ERROR ANALYSIS OF IMPLICIT-EXPLICIT ONE-LEG METHODS FOR STIFF VOLTERRA DELAY INTEGRO-DIFFERENTIAL EQUATIONS

Zhang Gengen1,2, Tang Lei2, Xiao Aiguo2   

  1. 1. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China;
    2. School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China
  • Received:2016-12-31 Online:2018-03-15 Published:2018-02-03
本文主要研究用隐显单支方法求解一类刚性Volterra延迟积分微分方程初值问题时的稳定性与误差分析。我们获得并证明了结论:若隐显单支方法满足2阶相容条件,且其中的隐式单支方法是A-稳定的,则隐显单支方法是2阶收敛且关于初值扰动是稳定的.最后,由数值算例验证了相关结论.
In this paper, we are focused on stability and error analysis of the implicit-explicit (IMEX) one-leg methods for stiff Volterra delay integro-differential equations. It is proven that if the IMEX one-leg methods is consistent of order $2$, and the corresponding implicit one-leg method is A-stable, then the IMEX one-leg methods are stable and convergent with order $2$. Numerical examples verify the validity of the obtained theoretical results.

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