ODE Software that Computes Guaranteed Bounds on the Solution

2000 ◽  
pp. 197-224 ◽  
Author(s):  
Nedialko S. Nedialkov ◽  
Kenneth R. Jackson
Keyword(s):  
Bounds On The Solution

Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equation

1986 ◽  
Vol 31 (7) ◽  
pp. 654-656 ◽  
Author(s):  
Sheng-De Wang ◽  
Te-Son Kuo ◽  
Chen-Fa Hsu
Keyword(s):  
Lyapunov Equation ◽  
Bounds On The Solution

scholarly journals Bounds on the Solution of Linear Time-Periodic Systems

PAMM ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 447-448 ◽  
Author(s):  
Peter Benner ◽  
Jonas Denißen ◽  
Ludwig Kohaupt
Keyword(s):  
Linear Time ◽  
Periodic Systems ◽  
Time Periodic ◽  
Bounds On The Solution

Solution Bounds for Transient Vibration Problems

1977 ◽  
Vol 44 (1) ◽  
pp. 159-164
Author(s):  
T. J. McDaniel ◽  
F. J. Testa ◽  
P. V. Thangam Babu
Keyword(s):  
Dynamic Systems ◽  
Iterative Procedure ◽  
Nonlinear Differential Equations ◽  
Lower Solution ◽  
Differential Inequalities ◽  
Initial Value ◽  
Transient Vibration ◽  
Vibration Problems ◽  
Two Degree Of Freedom ◽  
Bounds On The Solution

The theory of differential inequalities is applied to systems of nonlinear differential equations of the initial value type. Established bounding theorems are used to construct bounds on the solution of these equations and to develop an iterative procedure for improving these bounds. The methods are illustrated by constructing upper and lower solution bounds for one and two-degree-of-freedom dynamic systems.

Spectral Bounds on the Solution of Linear Time-Periodic Systems

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 863-864 ◽  
Author(s):  
Peter Benner ◽  
Jonas Denißen
Keyword(s):  
Linear Time ◽  
Periodic Systems ◽  
Spectral Bounds ◽  
Time Periodic ◽  
Bounds On The Solution
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