
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 : DEC 1966
Pagination or Media Count : 40
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 NewtonRaphson and Secant iteration methods. A modification of one of these theorems is given and applied to study the effect of roundoff errors in the NewtonRaphson and GaussSeidel 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