STUDIES IN NONLINEAR MODELING V: NONLINEAR MODELING FUNCTIONS OF A SPECIAL TYPE
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 n'th 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1962
- Accession Number
- AD0292106
Entities
People
- Otto George Ruehr
Organizations
- University of Michigan