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

@article{Gerdt2018TheMP, 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.}, year={2018}, volume={234}, pages={202-215} }

## 15 Citations

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

- Mathematics, Computer ScienceArXiv
- 2020

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

- Mathematics
- 2020

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

### Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2022

### Singularities of algebraic differential equations

- Mathematics, Computer ScienceAdv. Appl. Math.
- 2021

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

- MathematicsArXiv
- 2019

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

- Mathematics, Computer ScienceCASC
- 2022

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

- MathematicsJ. Syst. Sci. Complex.
- 2021

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

- Computer ScienceMath. Comput. Sci.
- 2021

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

- MathematicsACM Communications in Computer Algebra
- 2021

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…

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