The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEs

  title={The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEs},
  author={Vladimir P. Gerdt and Markus Lange-Hegermann and Daniel Robertz},
  journal={Comput. Phys. Commun.},

Strong Consistency and Thomas Decomposition of Finite Difference Approximations to Systems of Partial Differential Equations

An algorithmic approach that combines differential and difference algebra to analyze s(trong)-consistency of finite difference approximations of regular solution grids is suggested, which generalizes the definition given earlier for Cartesian grids.

Thomas Decomposition and Nonlinear Control Systems

The paper gives an introduction to the Thomas decomposition method and shows how notions such as invertibility, observability and flat outputs can be studied.

Periodic Pólya Urns, the Density Method, and Asymptotics of Young Tableaux

It is proved that the law of the south-east corner of a triangular Young tableau follows asymptotically a product of generalized gamma distributions, which allows us to tackle some questions related to the continuous limit of large random Young tableaux and links with random surfaces.

On boundary conditions parametrized by analytic functions

This work describes the necessary algorithms for Gr¨obner and Janet bases of Weyl algebras with certain analytic coefficients and provides examples of divergence-free functions in domains bounded by analytic functions and adapted to observations.

A Strongly-Consistent Difference Scheme for 3D Nonlinear Navier-Stokes Equations

The authors prove that, for strongly consistent difference scheme, each element in the difference Gröbner basis of such difference scheme always approximates a differential equation which vanishes on the analytic solutions of Navier-Stokes equations.

A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations

This work discusses the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic and demonstrates the relevance and applicability of this approach with computational experiments using a prototypical implementation in Reduce.

Maple application for structural identifiability analysis of ODE models

Structural identifiability properties of models of ordinary differential equations help one assess if the parameter's value can be recovered from experimental data. This theoretical property can be



Formal Algorithmic Elimination for PDEs

This tutorial discusses aspects of this correspondence between radical differential ideals and their analytic solution sets in differential algebra involving symbolic computation, and an introduction to the Thomas decomposition method is given.

Algebraically simple involutive differential systems and the Cauchy problem

We consider systems of polynomial nonlinear partial differential equations (PDEs) possessing certain properties. Such systems were studied by the American mathematician Thomas in the 1930s, and he

Reduction of systems of nonlinear partial differential equations to simplified involutive forms

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On Decomposition of Algebraic PDE Systems into Simple Subsystems

  • V. Gerdt
  • Mathematics, Computer Science
  • 2008
An algorithmization of the Thomas method for splitting a system of partial differential equations and (possibly) inequalities into triangular subsystems whose Thomas called simple is presented.


This paper studies triangular differential systems arising from various decompositions of partial differential polynomial systems. In theoretical aspects, we emphasizeon translating differential

Existence and uniqueness theorems for formal power series solutions of analytic differential systems

The idea is that an arbitrary noulincar system can be writed and allows its formal power series solut,ious t.0 lx coniput~ed in a11 alg0rithmic fashion.

Computing representations for radicals of finitely generated differential ideals

This paper deals with systems of polynomial differential equations, ordinary or with partial derivatives. The embedding theory is the differential algebra of Ritt and Kolchin. We describe an

Lagrangian Constraints and Differential Thomas Decomposition

The Differential Counting Polynomial

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