scholarly journals Symbolic Methods for Solving Algebraic Systems of Equations and Applications for Testing the Structural Stability

2020 ◽  
pp. 203-237
Author(s):  
Yacine Bouzidi ◽  
Fabrice Rouillier
Keyword(s):  
Structural Stability ◽  
Systems Of Equations ◽  
Algebraic Systems ◽  
Symbolic Methods

scholarly journals LISMA_HDS language for modeling heterogeneous dynamic systems

2021 ◽  
pp. 103-122
Author(s):  
Evgeny Popov ◽  
◽  
Yury Shornikov ◽  
Keyword(s):  
Dynamic Systems ◽  
Initial Value Problems ◽  
Method Of Lines ◽  
System Of Equations ◽  
Modeling Languages ◽  
Cauchy Problems ◽  
Systems Of Equations ◽  
Initial Value ◽  
Algebraic Systems ◽  
Different Types

Heterogeneous dynamic systems (HDS) simultaneously describe processes of different physical nature. Systems of this kind are typical for numerous applications. HDSs are characterized by the following features. They are often multimode or hybrid systems. In general, their modes are defined as initial value problems (Cauchy problems) for implicit differential-algebraic systems of equations. Due to the presence of heterogeneous dynamic components or processes evolving in both time and space, the dimension of the complete system of equations may be pretty high. In some cases, the system of equations has an internal structure, for instance, the differential-algebraic system of equations approximating a partial differential equation by the method of lines. An original huge system of equations can then be algorithmically rewritten in a compact form. Moreover, heterogeneous hybrid dynamical systems can generate events of qualitatively different types. Therefore one has to use different numerical event detection algorithms. Nowadays, HDSs are modeled and simulated in computer environments. The modeling languages widely used by engineers do not allow them to fully specify all the properties of the systems of this class. For instance, they do not include event typing constructs. That is why a declarative general-purpose modeling language named LISMA_HDS has been developed for the computer-aided modeling and ISMA simulation environment. The language takes into account all of the characteristic features of HDSs. It includes constructs for plain or algorithmic declaration of model constants, initial value problems for explicit differential-algebraic systems of equations, and initial guesses for variables. It also allows researchers to define explicit time events, modes and transitions between them upon the occurrence of events of different types, to use macros and implement event control. LISMA_HDS is defined by a generative grammar in an extended Backus-Naur form and semantic constraints. It is proved that the grammar belongs to the LL(2) subclass of context-free grammars.

Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras

Studia Logica ◽  
2011 ◽  
Vol 98 (1-2) ◽  
pp. 307-330
Author(s):  
J. P. Díaz Varela ◽  
B. F. López Martinolich
Keyword(s):  
Systems Of Equations ◽  
Algebraic Systems

Uncertainty quantification for algebraic systems of equations

2013 ◽  
Vol 128 ◽  
pp. 189-202 ◽  
Author(s):  
R.H. Lopez ◽  
L.F. Fadel Miguel ◽  
J.E. Souza de Cursi
Keyword(s):  
Uncertainty Quantification ◽  
Systems Of Equations ◽  
Algebraic Systems
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