Approximation of Zeros of Functions Arising in the Engineering Sciences.
Abstract
This thesis extends work which takes a function defined by a second order differential equation and determines an interval on which that function either has a zero or attains a minimum, bounded value. Theorems for locating zeros are proved for functions of a single real variable, functions of two real variables, and real vector-valued functions. Algorithms suitable for computer adaptation are presented in examples which locate zeros of such functions occurring in the engineering sciences as Legendre polynomials, Laguerre polynomials, Emden's equation, and Duffing's equation; special emphasis is given to the zeros of Bessel functions J sub n(X). The methods developed in this work are useful in optimization theory; they also can be used to obtain good initial approximations of zeros for starting iterative algorithms, such as the Newton-Raphson method, which give more exact zero values.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1977
- Accession Number
- ADA047783
Entities
People
- John W. Lukes
Organizations
- Air Force Institute of Technology