Related papers: Thomas Decomposition and Nonlinear Control Systems
This paper presents an algorithmic method to study structural properties of nonlinear control systems in dependence of parameters. The result consists of a description of parameter configurations which cause different control-theoretic…
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…
We present the Maple package TDDS (Thomas Decomposition of Differential Systems). Given a polynomially nonlinear differential system, which in addition to equations may contain inequations, this package computes a decomposition of it into a…
For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach that combines differential and difference algebra to analyze s(trong)-consistency of finite difference approximations.…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…
Decomposition, statically dividing a program into multiple units, is a common programming technique for realizing parallelism and refining programs. The decomposition of a sequential program into components is tedious, due to the…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach to the s(trong)-consistency analysis of their finite difference approximations on Cartesian grids. First we apply the…
In this paper we are going to make an analytical and numerical analysis for the Thomas system. Physically, this system describes a particle, driving by a system of oscillators, dissipated by a dissipation term b > 0. Mathematically, this…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…
We describe a method to analyze and decompose the dynamics of a control system on a Lie group subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Differential-elimination algorithms apply a finite number of differentiations and eliminations to systems of partial differential equations. For systems that are polynomially nonlinear with rational number coefficients, they guarantee the…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…
In this work, we present a distributed framework based on the graph algorithm for computing control invariant set for nonlinear cascade systems. The proposed algorithm exploits the structure of the interconnections within a process network.…