圆域上四阶方程及其特征值问题基于降阶格式的谱Galerkin逼近.pdf

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摘要···················································································III

Abstract····················································································IV

1绪论·······················································································1

2预备知识介绍·········································································3

2.1Jacobi多项式和Legendre多项式的基本性质···················3

2.2多项式逼近空间···························································4

2.3Fourier基函数·······························································5

3圆域上简支板边界条件下四阶问题基于降阶格式的谱Galerkin逼

近·····························································································7

3.1四阶问题及其降阶格式·················································7

3.2弱形式及其谱Galerkin逼近···········································9

3.3解的存在唯一性和误差估计··········································11

3.4算法实现和数值算例····················································21

4圆域上简支板边界条件下四阶特征值问题基于降阶格式的

谱Galerkin逼近·········································································27

4.1问题描述与降阶格式····················································27

4.2弱形式和谱Galerkin逼近···············································27

4.3算法实现······································································28

4.4数值算例······································································29

5一维四阶方程基于降阶格式的谱Galerkin逼近及误差估计·······32

5.1降阶格式及其变分形式·················································32

5.2逼近解的误差估计································

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