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计算数学  2018, Vol. 40 Issue (1): 33-48    DOI:
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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. 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
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. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China;
2. School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China
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摘要 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.
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关键词隐显单支方法   刚性问题   Volterra延迟积分微分方程   误差分析   稳定性     
Abstract: 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.
Key wordsImplicit-explicit one-leg methods   Stiff problems   Volterra delay integro-differential equations   Error analysis   Stability   
收稿日期: 2016-12-31;
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.

引用本文:   
. 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.
. 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.
 
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