TDDS
The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEs. 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 finite set of differentially triangular and algebraically simple subsystems whose subsets of equations are involutive. Usually the decomposed system is substantially easier to investigate and solve both analytically and numerically. The distinctive property of a Thomas decomposition is disjointness of the solution sets of the output subsystems. Thereby, a solution of a well-posed initial problem belongs to one and only one output subsystem. The Thomas decomposition is fully algorithmic. It allows to perform important elements of algebraic analysis of an input differential system such as: verifying consistency, i.e., the existence of solutions; detecting the arbitrariness in the general analytic solution; given an additional equation, checking whether this equation is satisfied by all common solutions of the input system; eliminating a part of dependent variables from the system if such elimination is possible; revealing hidden constraints on dependent variables, etc. Examples illustrating the use of the package are given.
Keywords for this software
References in zbMATH (referenced in 7 articles )
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Sorted by year (- Lange-Hegermann, Markus; Robertz, Daniel; Seiler, Werner M.; Seiß, Matthias: Singularities of algebraic differential equations (2021)
- Seiler, Werner M.; Seiß, Matthias; Sturm, Thomas: A logic based approach to finding real singularities of implicit ordinary differential equations (2021)
- Zhang, Xiaojing; Chen, Yufu: A strongly-consistent difference scheme for 3D nonlinear Navier-Stokes equations (2021)
- Banderier, Cyril; Marchal, Philippe; Wallner, Michael: Periodic Pólya urns, the density method and asymptotics of Young tableaux (2020)
- Lange-Hegermann, Markus; Robertz, Daniel: Thomas decomposition and nonlinear control systems (2020)
- Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Michels, Dominik L.: On the algorithmic linearizability of nonlinear ordinary differential equations (2020)
- Quadrat, Alban (ed.); Zerz, Eva (ed.): Algebraic and symbolic computation methods in dynamical systems. Based on articles written for the invited sessions of the 5th symposium on system structure and control, IFAC, Grenoble, France, February 4--6, 2013 and of the 21st international symposium on mathematical theory of networks and systems (MTNS 2014), Groningen, the Netherlands, July 7--11, 2014 (2020)