An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system

1997 ◽  
Vol 8 (1) ◽  
pp. 1-23 ◽  
Author(s):  
M. A. Barkatou
Keyword(s):  
Differential System ◽  
Fundamental Matrix ◽  
Linear Differential System ◽  
Matrix Solution ◽  
Fundamental Matrix Solution ◽  
Linear Differential ◽  
Exponential Part

Characterizations of linear differential systems with a regular singular point

1972 ◽  
Vol 18 (2) ◽  
pp. 93-98 ◽  
Author(s):  
W. A. Harris
Keyword(s):  
Singular Point ◽  
Differential System ◽  
Fundamental Matrix ◽  
Linear Differential System ◽  
Regular Singular Point ◽  
Constant Matrix ◽  
Linear Differential Systems ◽  
Significant Difference ◽  
Linear Differential ◽  
Image Position

The linear differential systemwhere w is a vector with n components and A is an n by n matrix is said to have z = 0 as a regular singular point if there exists a fundamental matrix of the formsuch that S is holomorphic at z = 0 and R is a constant matrix ((1), p. 111; (2), p. 73). For such systems A will have at most a pole at z = 0 and we may writewhere p is an integer, Ã is holomorphic at z = 0, and Ã(0) ≠ 0. However, the converse is not true. When p ≦ − 1, A is holomorphic at z = 0, and every fundamental matrix is holomorphic at z = 0. If p ≧ 1, the non-negative integer p is called (after Poincaré) the rank of the singularity and there is a significant difference between the cases p = 0 and p ≧ 1. If p = 0 the linear differential system (1) is known to have z = 0 as a regular singular point ((1), p. 111) ; whereas, if p ≧ 1, z = 0 may or may not be a regular singular point.

scholarly journals On a linear differential system of neutral type

1986 ◽  
Vol 40 (2) ◽  
pp. 226-233
Author(s):  
P. Ch. Tsamatos
Keyword(s):  
Fixed Points ◽  
Differential System ◽  
Finite Dimension ◽  
Neutral Type ◽  
Common Fixed Points ◽  
Linear Differential System ◽  
Linear Differential

AbstractThis paper is concerned with the neutral type differential system with derivating arguments. By decomposing the space of initial functions into classes, it is derived that, for each class, the space of corresponding solutions is of finite dimension. The case of common fixed points of the arguments is also studied.

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