The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEs
Abstract
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 wellposed 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.
 Publication:

Computer Physics Communications
 Pub Date:
 January 2019
 DOI:
 10.1016/j.cpc.2018.07.025
 arXiv:
 arXiv:1801.09942
 Bibcode:
 2019CoPhC.234..202G
 Keywords:

 Differential system;
 Thomas decomposition;
 Simple system;
 Completion to involution;
 Differential elimination;
 Consistency;
 Physics  Computational Physics;
 Mathematics  Commutative Algebra;
 Mathematics  Analysis of PDEs
 EPrint:
 doi:10.1016/j.cpc.2018.07.025