Accession Number : AD0726413

Title :   Analytic Simplification of a System of Ordinary Differential Equations at an Irregular-Type Singularity.

Descriptive Note : Final rept.,

Corporate Author : NAVAL RESEARCH LAB WASHINGTON D C MATHEMATICS RESEARCH CENTER

Personal Author(s) : Hsieh,Po-Fang

Report Date : 11 JUN 1971

Pagination or Media Count : 35

Abstract : Let l sub n (u) = diag ((u sub 1), ..., (u sub n)) for given complex (u sub k). If Re (u sub k) = or > 0 (1 = or < k = or < n), then the (m+n)-system (x to the power (sigma +1)) y' = F(x,z)y,xz = (l sub n)z is simplified to (x to the power (sigma + 1))Y' = G(x,Z)Y, xZ' = (l sub n) (u)Z by a transformation T defined as y = Y + P(x,Z)Y,z = Z in a sector having property T with respect to ((lambda sub i)-(lambda sub j)(oxo)/(sigma(x to the power sigma))/i, j = 1, ..., s, (i not equal to j)), where (lambda sub i) (i = 1,2,...,s) are distinct eigenvalues of F(0,0) and G(x,Z) is in block-diagonal form agreeing with the Jordan canonical form of F(0,0). (Author)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, COMPLEX VARIABLES), TRANSFORMATIONS(MATHEMATICS), MATRICES(MATHEMATICS), INTEGRAL EQUATIONS, NUMERICAL INTEGRATION, ASYMPTOTIC SERIES, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE