本文主要研究内容
作者王彩珍（2019）在《非线性偏微分方程的重心插值配点法》一文中研究指出：无网格方法是近年来被广泛应用的一种数值计算方法,重心插值配点法是一种高精度的无网格数值计算方法。目前,重心插值配点法主要用于求解线性偏微分方程,但对非线性偏微分方程的离散方程难以处理。鉴于此,本文在重心插值配点法的基础上,通过构造直接线性化迭代和Newton-Raphson迭代来对非线性椭圆型方程和非线性抛物型方程进行离散,使得重心插值配点法更具通用性。通过若干非线性偏微分方程的数值模拟,比较本文所构造的两种方法的误差,验证不同方法的优劣。因此,本文所做的研究工作如下:基于非线性椭圆型方程和非线性抛物型方程,将两种迭代法应用在两类偏微分方程上。首先利用重心插值配点法构造出非线性椭圆型方程和非线性抛物型方程所对应的离散方程;其次将线性化迭代和Newton-Raphson迭代应用到所对应的离散方程中,写出各离散方程对应的线性化迭代格式和Newton-Raphson迭代格式;再对边界条件进行离散;最后得出非线性偏微分方程所对应的近似解。结果表明:(1)本文所构造的两种迭代法在求解非线性偏微分方程都可达到较高的计算精度;(2)比较两种迭代法的计算结果,Newton-Raphson迭代法求解非线性偏微分方程具有高精度、高效率、无条件稳定的特性;(3)比较重心Lagrange插值和重心有理插值的计算结果,重心Lagrange插值精度更高,稳定性更强,易在非线性偏微分方程的求解中被采用。
Abstract
mo wang ge fang fa shi jin nian lai bei an fan ying yong de yi chong shu zhi ji suan fang fa ,chong xin cha zhi pei dian fa shi yi chong gao jing du de mo wang ge shu zhi ji suan fang fa 。mu qian ,chong xin cha zhi pei dian fa zhu yao yong yu qiu jie xian xing pian wei fen fang cheng ,dan dui fei xian xing pian wei fen fang cheng de li san fang cheng nan yi chu li 。jian yu ci ,ben wen zai chong xin cha zhi pei dian fa de ji chu shang ,tong guo gou zao zhi jie xian xing hua die dai he Newton-Raphsondie dai lai dui fei xian xing tuo yuan xing fang cheng he fei xian xing pao wu xing fang cheng jin hang li san ,shi de chong xin cha zhi pei dian fa geng ju tong yong xing 。tong guo re gan fei xian xing pian wei fen fang cheng de shu zhi mo ni ,bi jiao ben wen suo gou zao de liang chong fang fa de wu cha ,yan zheng bu tong fang fa de you lie 。yin ci ,ben wen suo zuo de yan jiu gong zuo ru xia :ji yu fei xian xing tuo yuan xing fang cheng he fei xian xing pao wu xing fang cheng ,jiang liang chong die dai fa ying yong zai liang lei pian wei fen fang cheng shang 。shou xian li yong chong xin cha zhi pei dian fa gou zao chu fei xian xing tuo yuan xing fang cheng he fei xian xing pao wu xing fang cheng suo dui ying de li san fang cheng ;ji ci jiang xian xing hua die dai he Newton-Raphsondie dai ying yong dao suo dui ying de li san fang cheng zhong ,xie chu ge li san fang cheng dui ying de xian xing hua die dai ge shi he Newton-Raphsondie dai ge shi ;zai dui bian jie tiao jian jin hang li san ;zui hou de chu fei xian xing pian wei fen fang cheng suo dui ying de jin shi jie 。jie guo biao ming :(1)ben wen suo gou zao de liang chong die dai fa zai qiu jie fei xian xing pian wei fen fang cheng dou ke da dao jiao gao de ji suan jing du ;(2)bi jiao liang chong die dai fa de ji suan jie guo ,Newton-Raphsondie dai fa qiu jie fei xian xing pian wei fen fang cheng ju you gao jing du 、gao xiao lv 、mo tiao jian wen ding de te xing ;(3)bi jiao chong xin Lagrangecha zhi he chong xin you li cha zhi de ji suan jie guo ,chong xin Lagrangecha zhi jing du geng gao ,wen ding xing geng jiang ,yi zai fei xian xing pian wei fen fang cheng de qiu jie zhong bei cai yong 。
论文参考文献
论文详细介绍
论文作者分别是来自长安大学的王彩珍，发表于刊物长安大学2019-11-04论文，是一篇关于非线性椭圆型方程论文,非线性抛物型方程论文,重心插值论文,重心有理插值论文,长安大学2019-11-04论文的文章。本文可供学术参考使用，各位学者可以免费参考阅读下载，文章观点不代表本站观点，资料来自长安大学2019-11-04论文网站，若本站收录的文献无意侵犯了您的著作版权，请联系我们删除。
标签：非线性椭圆型方程论文; 非线性抛物型方程论文; 重心插值论文; 重心有理插值论文; 长安大学2019-11-04论文;