Preservation of equilibrium states and their stability for discrete Runge-Kutta approximations of continuous systems

1996 ◽  
Vol 59 (5) ◽  
pp. 568-571
Author(s):  
L. Z. Fishman
Keyword(s):  
Equilibrium States ◽  
Continuous Systems ◽  
Runge Kutta

scholarly journals Tool Presentation: Isabelle/HOL for Reachability Analysis of Continuous Systems

10.29007/b3wr ◽  
2018 ◽  
Author(s):  
Fabian Immler
Keyword(s):  
Distinctive Feature ◽  
Reachability Analysis ◽  
Theorem Prover ◽  
Continuous Systems ◽  
Affine Arithmetic ◽  
Discretization Errors ◽  
Runge Kutta

We present a tool for reachability analysis of continuous systems based onaffine arithmetic and Runge-Kutta methods. The distinctive feature of our toolis its verification in the interactive theorem prover Isabelle/HOL: thealgorithm is guaranteed to compute safe overapproximations, taking into accountall round-off and discretization errors.

Macroeconomic Equilibrium Theory in the Context of Methodological Problems of Contemporary Economic Science

2008 ◽  
pp. 77-88
Author(s):  
M. Likhachev
Keyword(s):  
Empirical Analysis ◽  
Equilibrium States ◽  
Equilibrium Theory ◽  
Economic Systems ◽  
Economic Science ◽  
The Real ◽  
Theoretical Status ◽  
Methodological Problems ◽  
Real Stability

The article is devoted to the analysis of methodological problems in using the conception of macroeconomic equilibrium in contemporary economics. The author considers theoretical status and relevance of equilibrium conception and discusses different areas and limits of applicability of the equilibrium theory. Special attention is paid to different epistemological criteria for this theory taking into account both empirical analysis of the real stability of economic systems and the problem of unobservability of equilibrium states.

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