NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE'sIf a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.
Document ID
19770021843
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Geddes, K. O.
(Waterloo Univ. Ontario)
Date Acquired
August 8, 2013
Publication Date
January 1, 1977
Publication Information
Publication: NASA. Langley Res. Center Proc. of the 1977 MACSYMA Users' Conf. (NASA)
Subject Category
Numerical Analysis
Accession Number
77N28787
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

Available Downloads

There are no available downloads for this record.
No Preview Available