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一种求解时滞微分方程的小波方法
  • ISSN号：0455-2059
  • 期刊名称：兰州大学学报(自然科学版)
  • 时间：2011
  • 页码：87-90+96
  • 分类：O241[理学—计算数学;理学—数学]
  • 作者机构：[1]兰州大学西部灾害与环境力学教育部重点实验室,土木工程与力学学院,兰州730000
  • 相关基金：基金项目：国家自然科学基金青年基金项目（10802034）,国家自然科学基金项目（10972094）
  • 相关项目：超导电-磁-热-力多场耦合非线性力学的基础理论与实验研究
作者： 刘小靖|周又和|周俊|
关键词： 线性时滞微分方程, SHANNON小波, 小波配点法, 初值问题, 高精度, linear time-delayed differential equation, Shannon wavelet, wavelet collocation method, initial-value problem, high accuracy
中文摘要：

提出了一种基于小波理论的求解线性时滞微分方程的数值方法，该方法将线性时滞微分方程的解在求解区域内展开为小波尺度函数级数，再利用配点法将时滞微分方程的初值问题转化为线性代数方程组的求解问题．与传统的逐步数值积分方法相比，该方法将方程的解在求解区域内做全局小波近似，因而具有全局误差可控的优点，从而有效地克服了逐步数值积分法所固有的误差积累的缺陷，并具有很高的精度．

英文摘要：

A new numerical method based on wavelets was proposed for solving linear ordinary differential equations with time delays. In the proposed method wavelet approximation was established for the solution of time-delayed ordinary differential equations, and then the initial-value problem of time-delayed ODE was equivalently transformed to a linear algebraic equation by applying the wavelet collocation method. Because the wavelet approximation of solution is a global expression, the global error of solution can be controlled and the cumulative error eliminated, as compared with conventional step-by-step methods. The proposed method has high accuracy.

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超磁致伸缩材料的时变本构关系及其智能控制应用的基础研究
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超导电-磁-热-力多场耦合非线性力学的基础理论与实验研究
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期刊信息
  • 《兰州大学学报：自然科学版》
  • 中国科技核心期刊
  • 主管单位:教育部
  • 主办单位:兰州大学
  • 主编：涂永强
  • 地址：兰州市天水南路222号
  • 邮编：730000
  • 邮箱：jns@lzu.edu.cn
  • 电话：0931-8912707
  • 国际标准刊号：ISSN：0455-2059
  • 国内统一刊号：ISSN：62-1075/N
  • 邮发代号:54-3
  • 获奖情况:
  • 全国自然科学类核心期刊,甘肃省优秀科技期刊
  • 国内外数据库收录:
  • 美国化学文摘（网络版）,美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,英国动物学记录,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,英国英国皇家化学学会文摘,中国北大核心期刊（2000版）
  • 被引量:12892