Accession Number:

AD0292106

Title:

STUDIES IN NONLINEAR MODELING V: NONLINEAR MODELING FUNCTIONS OF A SPECIAL TYPE

Descriptive Note:

Corporate Author:

MICHIGAN UNIV ANN ARBOR RADIATION LAB

Personal Author(s):

Report Date:

1962-08-01

Pagination or Media Count:

1.0

Abstract:

This paper discusses the nonlinear modeling of three types of partial differential equations in n variables, elliptic, parabolic, and hyperbolic. The modeling functions are restricted to depend only on the measured dependent variable and not on the coordinates. For the scalar wave equation elliptic and the diffusion equation parabolic it is found that the allowable modeling functions must satisfy a particular nth order nonlinear ordinary differential equation. A simple counter-example shows that similar restrictions do not hold for the time-dependent wave equation hyperbolic. The sets of allowable modeling functions corresponding to the wave and diffusion equations are shown to be identical to those obtained by modeling certain second order linear ordinary differential equations. The problem of similitude restrictions is interpreted as the study of certain polynomials generated by Burmann series expansions. The limiting behavior of these polynomials is obtained in special cases. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE