Accession Number:

AD0653013

Title:

SOME STABILITY THEOREMS FOR ORDINARY DIFFERENCE EQUATIONS.

Descriptive Note:

Technical rept.,

Corporate Author:

BROWN UNIV PROVIDENCE R I CENTER FOR DYNAMICAL SYSTEMS

Personal Author(s):

• Hurt,James

Report Date:

1966-12-01

Pagination or Media Count:

40.0

Abstract:

LaSalle and others have developed a generalization of the second method of Liapunov which utilizes certain invariance properties of solutions of ordinary differential equations. Invariance properties of solutions of ordinary difference equations are utilized here to develop stability theorems similar to those in LaSalle. As illustrations of the application of these theorems, a region of convergence is derived for the Newton-Raphson and Secant iteration methods. A modification of one of these theorems is given and applied to study the effect of roundoff errors in the Newton-Raphson and Gauss-Seidel iteration methods.

Descriptors:

• (*DIFFERENCE EQUATIONS
• *THEOREMS)
• (*DIFFERENTIAL EQUATIONS
• STABILITY)
• INVARIANCE
• CONVERGENCE
• ITERATIONS
• ERRORS
• OPERATORS(MATHEMATICS)
• SEQUENCES(MATHEMATICS)
• FUNCTIONS(MATHEMATICS)
• SET THEORY

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE