THE ROLE OF ORTHOGONAL POLYNOMIALS IN NUMERICAL ORDINARY DIFFERENTIAL-EQUATIONS

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:43

Article

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;   

DOI  :  10.1016/0377-0427(92)90268-3

来源: Elsevier

【 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.

【 授权许可】

Free