计算数学
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计算数学  2017, Vol. 39 Issue (4): 351-362    DOI:
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一类弱奇性Volterra积分微分方程的级数展开数值解法
古振东, 孙丽英
广东金融学院应用数学系, 广州 510521
SERIES EXPANSION METHOD FOR WEAKLY SINGULAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
Gu Zhengdo, Sun Liying
Guangdong University of Finance Guangzhou 510521, China
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摘要 本文考察了一类弱奇性积分微分方程的级数展开数值解法,并给出了相应的收敛性分析.理论分析结果表明,若用已知函数的谱配置多项式逼近已知函数,那么方程的数值解以谱精度逼近方程的真解.数值实验数据也验证了这一理论分析结果.
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关键词Volterra积分微分方程   谱配置逼近   级数展开   收敛性分析     
Abstract: In this paper, we investigate the series expansion method for weakly singular Volterra integro-differential equations. The provided convergence analysis shows that if given functions is approximated by their own spectral collocation polynomials, then numerical solution converge to exact solution at the rate of spectral accuracy. Numerical experiments are carried out to confirm this result.
Key wordsVolterra integro-differential equations   spectral collocation approximation   series expansion   convergence analysis   
收稿日期: 2016-12-22;
基金资助:

广东省自然科学基金项目(2017A030310636),广东省高性能计算学会开放课题基金项目(2017060104),中山大学广东省计算科学重点实验室开放基金项目(2016001,2016006),广东省高等学校优秀青年教师培养计划项目(YQ201403),广东高校省级重点平台和重大科研项目(2015GXJK101)和广东金融学院金融数据挖掘与量化投资创新团队项目资助.

引用本文:   
. 一类弱奇性Volterra积分微分方程的级数展开数值解法[J]. 计算数学, 2017, 39(4): 351-362.
. SERIES EXPANSION METHOD FOR WEAKLY SINGULAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2017, 39(4): 351-362.
 
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