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广义Laguerre函数的拟谱方法及其应用

科学与工程中的许多问题可归结为无界区域中数学物理方程的定解问题。对这类问题的求解,最简单的方法是先取定某个人工边界,给出适当的人工边界条件,然后在相应的有界区域中用通常的方法,例如有限差分方法、有限元方法或者谱方法等数值方法求解。然而,这种截断必然会带来相应的误差。因此需要研究直接计算无界区域上的数学物理问题的高精度算法。正是在这样的背景下,本文提出了一种求解无界区域问题的数值方法,即广义Laguerre函数的拟谱方法。我们的研究由以下几部分组成。首先,我们介绍了广义Laguerre多项式逼近的一些基本结果。在第三章,我们建立了广义Laguerre函数插值逼近的一些基本结果。第四章是这种新方法的一些应用。我们首先考虑了全平面上的定常对称问题,建立了相应的拟谱格式,并证明了格式的收敛性。然后我们研究了单位圆外部的对称问题,建立了相应的拟谱格式,并证明了格式的收敛性。在第五章,我们给出相应的数值结果,这些结果表明了这种新方法是非常有  (本文共39页) 本文目录 | 阅读全文>>

《Journal of Systems Science & Complexity》2018年03期
Journal of Systems Science & Complexity

Optimal Multimodel Representation by Laguerre Filters Applied to a Communicating Two Tank System

This paper presents the development of a new nonlinear representation by exploiting the multimodel approach and the new linear representation ARX-Laguerre for each operating region. The resulting multimodel, entitled ARX-Laguerre multimodel, is characterized by the parameter number reduction with a recursive representation. However, a significant r...  (本文共26页) 阅读全文>>

《Acta Mathematica Sinica》2016年06期
Acta Mathematica Sinica

Complete Hypersurfaces with Constant Laguerre Scalar Curvature in R~n

Let x:M~(n-1)→R~n be an umbilical free hypersurface with non-zero principal curvatures.Two basic invariants of M under the Laguerre transformation group of R~n are Laguerre form C and Laguerre tensor L.In this paper,we prove the following theorem:Let M be an(...  (本文共10页) 阅读全文>>

《Acta Mathematica Sinica》2015年03期
Acta Mathematica Sinica

On Laguerre Form and Laguerre Isoparametric Hypersurfaces

Let x : Mn-1→ Rnbe an umbilical free hypersurface with non-zero principal curvatures.M is called Laguerre isoparametric if it satisfies two conditions, namely, it has vanishing Laguerre form and ha...  (本文共10页) 阅读全文>>

《Acta Mathematica Sinica》2014年01期
Acta Mathematica Sinica

Laguerre Isoparametric Hypersurfaces in R~n with Two Distinct Non-zero Principal Curvatures

An umbilical free oriented hypersurfacex:M→Rnwith non-zero principal curvatures is called a Laguerre isoparametric hypersurface if its Laguerre form C=i Ciωi=iρ1(Ei(logρ)(r ri)Ei(r))ωi vanishes and Laguerre shape operator S=ρ1(S 1 rid)has constant...  (本文共12页) 阅读全文>>

《Journal of Wuhan University of Technology(Materials Science Edition)》2014年01期
Journal of Wuhan University of Technology(Materials Science Edition)

Laguerre Simulation and Visualization for Microstructure of Metal Materials

Simulation method was designed to divide Laguerre diagram for right circle group with different weight; out-of-core incremental algorithm for Laguerre diagram was constructed; simulation program development and visualization was done and simulation was rea...  (本文共4页) 阅读全文>>