## 加权余量法及其在微分方程中的应用

Application of the method of weighted residuals and in differential equations
Abstract: the method of weighted residuals is a kind of directly from the differential equations and boundary conditions, numerical calculation method for boundary value problem of the approximate solution of the important. The method of weighted residuals approximation in solving differential equations have important applications in the solution, this paper first has carried on the simple introduction about the method of weighted residuals, explained the basic theory of the method, because the method to take the weight function is different, so get some special weighted residual method, the common steps and through the study on the application of weighted residuals method to get the solution of differential equation, finally through several examples in order to explain the use of the method of weighted residuals different approximate solutions applied in solving the differential equation.
Key Words: weighted residual method; numerical method; differential equation

1 基础知识    3
1．1 偏微分方程的定义    3 源￥自%六^^维*论-文+网=www.lwfree.cn
1．2 加权余量法的基本理论    4
2 加权余量法的几种特殊情况    5
2. 1迦辽金法    5
2. 2矩法.    5
2. 3配置法    5
2. 4子区域法.. .6
3加权余量法在解微分方程近似解中的应用举例    7
4 结束语    15

文献[3]详细的论述了加权余量法的理论方法与应用，是在求解微分方程近似解的一个借鉴和参考，文献[2]介绍加权余量法在国内外的发展状况以及在其他方面的应用，文献[4]通过对加权余量法和边界元法的比较，得出加权余量法的优势之处.本文结合文献[3][4][5][6][8]详细的给出了加权余量法的基本概念和几种比较常用的方法的具体应用，我国加权余量法的应用已经从静力发展到动力、稳定、材料非线性和几何非线性等各个问题中. 源￥自%六^^维*论-文+网=www.lwfree.cn

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