四阶方程的有理Legendre函数全对角化谱方法  

A Fully Diagonalized Legendre Rational Spectral Method for Solving Fourth Order Equations

作　　者：李珊[1] 栗巧玲 LI Shan;LI Qiaoling(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院，上海 200093

出　　处：《上海理工大学学报》2019年第5期422-428,共7页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11601331,11701119)

摘　　要：针对四阶椭圆型方程,提出了在半直线域上全对角化的有理Legendre谱方法。构造了Sobolev正交的Legendre有理基函数,并导出了相应的全对角化的离散代数方程组。与此同时,微分方程的真解和数值解都表示为Fourier级数形式及其截断形式。数值结果表明了该方法的高效性并保持谱精度。A fully diagonalized Legendre rational spectral method for solving fourth order elliptic equations on the half line was proposed.Some Sobolev orthogonal Legendre rational basis functions were constructed which leaded to the diagonalization of discrete systems.Accordingly,both the exact solutions and the approximate solutions could be represented as infinite and truncated Fourier series.Numerical results demonstrate the effectiveness and the spectral accuracy.

关 键 词：四阶椭圆型方程 有理Legendre谱方法 Sobolev正交 半直线 

分 类 号：O175[理学—数学]