THE ROLE OF ORTHOGONAL POLYNOMIALS IN NUMERICAL ORDINARY DIFFERENTIAL-EQUATIONS

被引：9
作者：
BUTCHER, JC
机构：
[1] Department of Mathematics and Statistics, University of Auckland
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1992年 / 43卷 / 1-2期
关键词：
ORTHOGONAL POLYNOMIALS; ORDINARY DIFFERENTIAL EQUATIONS; LEGENDRE POLYNOMIALS; JACOBI POLYNOMIALS; LAGUERRE POLYNOMIALS; CHEBYSHEV POLYNOMIALS; RUNGE-KUTTA METHODS; GAUSSIAN QUADRATURE; RADAU QUADRATURE; LOBATTO QUADRATURE; STIFF PROBLEMS; IMPLEMENTATION COSTS;
D O I：
10.1016/0377-0427(92)90268-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Orthogonal polynomials have many applications to numerical ordinary differential equations. Some of these, especially those connected with the quadrature formulae on which many differential equation methods are based, are to be expected. On the other hand, there are many surprising applications, quite unlike traditional uses of orthogonal polynomials. This paper surveys many of these applications, especially those related to accuracy and implementability of Runge-Kutta methods.
引用
收藏
页码：231 / 242
页数：12
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