谱方法解微分方程.pdf

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1、目录1.谱方法解微分方程............................................................................................................................11.1解微分方程的加权余量法(METHODSOFWEIGHTRESIDUALS)...................................................11.1.1基本思想...............................

2、...............................................................................................11.1.2MWR的基本方法..................................................................................................................21.2正交函数系与谱近似.................................

3、.................................................................................31.2.1正交函数系与正交多项式..................................................................................................31.2.2谱近似................................................................

4、..................................................................41.3谱方法求解微分方程..................................................................................................................51.3.1ChebyshevGalerkin方法...................................................

5、..................................................51.3.2ChebyshevTau........................................................................................................................51.3.3ChebyshevCollocation方法.....................................................

6、.............................................62.谱元方法(THESPECTRALELEMENTMETHOD)....................................................................62.1有限元方法与谱方法比较...........................................................................................................6

7、2.2变分原理.......................................................................................................................................72.2.1常微分方程边值问题的Galerkin变分原理........................................................................72.2.2偏微分方程的Galerkin变分原理...

8、.....................................................................................82.2.3非齐次边界条件的处理................