分数积分的一种数值计算方法及其应用

朱正佑; 李根国; 程昌钧

分数积分的一种数值计算方法及其应用

1.
上海大学上海市应用数学和力学研究所, 上海 200072;
2.
上海大学数学系, 上海 200072;
3.
上海大学力学系, 上海 200072;
4.
上海超级计算中心, 上海 201203

基金项目: 国家自然科学基金(60273048);上海市科学技术发展基金(98JC14032);上海市教委发展基金(99A01)

详细信息

作者简介:
朱正佑(1937- ),男,浙江海盐人,教授,博士生导师(E-mail:zyzhu@mail.shu.edu.cn);李根国(1969- ),男,甘肃古浪人,博士,现从事并行计算方法研究(E-mail:ggli@ssc.net.cn).

中图分类号: O165.6;O345
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- 文章访问数: 2801
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出版历程
- 收稿日期: 2001-10-30
- 修回日期: 2003-01-06
- 刊出日期: 2003-04-15

A Numerical Method for Fractional Integral With Applications

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
2.
Department of Mathematics, Shanghai University, Shanghai 200072, P. R. China;
3.
Department of Mechanics, Shanghai University, Shanghai 200072, P.R. China;
4.
Shanghai Supercomputer Center, Shanghai 201203, P. R. China

摘要

摘要: 提出了一种只需要存储部分历史数据的分数积分的数值计算方法,并给出了误差估计。这种方法可对包含分数积分和分数导数的积分-微分方程进行较长时间的数值计算,克服了存储全部历史数据的困难,并能对计算误差进行控制。作为应用,给出了具有分数导数型本构关系的粘弹性Timoshenko梁的动力学行为研究的控制方程,利用分离变量法讨论梁在简谐激励作用下的动力响应,然后用新提出的数值方法对控制方程进行数值计算,数值计算结果和理论结果进行了比较,它们比较吻合。
- 分数微积分 /
- 数值计算方法 /
- 分数导数型本构关系 /
- 弱奇异性Volterra积分-微分方程
Abstract: A new numerical method for the liactional integral that only stores part history data is preseated, and its discretization error is estimated.The method can be used to solve the integno-diffemntial equation including fiactional integral or fractional derivative in a long history.The difficulty of storing all history data is overcoane and the error can be controlled. As application, motion equations goverring the dynandcal behavior of a viscoelastic Timoshenko beam with fractional derivative constitutiverelation are gniven.The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables metiwd. Then the new numerical method is used to solve a class of wealdy singular Voltena integro-differential equations which are applied to descaibe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmeiical results are compared.It is foiurd that they are very close.
- fiactional calculus /
- rnumerical method /
- fiactional derivative constitutive relation /
- weakly singular Voltema integro-differential equation

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参考文献(19)

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[9]	Enelund M,Olsson P.Damping described by fading memory-analysis and application to fractional derivative models[J].Int J Solids Strut,1999,36(5):939-970.
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[11]	程昌钧,张能辉.横向周期载荷作用的粘弹性矩形板的混沌和超混沌运动[J].力学学报,1998,30(6):690-699.
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分数积分的一种数值计算方法及其应用

作者简介:
朱正佑(1937- ),男,浙江海盐人,教授,博士生导师(E-mail:zyzhu@mail.shu.edu.cn);李根国(1969- ),男,甘肃古浪人,博士,现从事并行计算方法研究(E-mail:ggli@ssc.net.cn).

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A Numerical Method for Fractional Integral With Applications

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留言板

分数积分的一种数值计算方法及其应用

作者简介: 朱正佑(1937- ),男,浙江海盐人,教授,博士生导师(E-mail:zyzhu@mail.shu.edu.cn);李根国(1969- ),男,甘肃古浪人,博士,现从事并行计算方法研究(E-mail:ggli@ssc.net.cn).

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出版历程

A Numerical Method for Fractional Integral With Applications

计量

出版历程

目录

作者简介:
朱正佑(1937- ),男,浙江海盐人,教授,博士生导师(E-mail:zyzhu@mail.shu.edu.cn);李根国(1969- ),男,甘肃古浪人,博士,现从事并行计算方法研究(E-mail:ggli@ssc.net.cn).