Documentation of the computer program performing computer assisted proof of existence of globally attracting fixed points of the viscous Burgers equation.

Jacek Cyranka

Updated: 23 Dec 2013

contact addresses: jcyranka (at) g mail , jcyranka (at)
www: my home page

The zipped program package
Numerical data from the proofs
Supplementary material (pdf file with some estimates, algorithms and proofs that were excluded from the paper)

Directory structure

Compile instructions

The program has been written in C++ programming language. It makes use of the CAPD library. Version dated 2010-12-29 comes along with the program in the package . Preferred compiler is GCC (tested to be compatible with versions 4.6.3, but the program is incompatible with newer GCC like 4.7). When newer GCC compiler is used the program should be compiled using g++-4.6 command. The rules of compiling are the same as for the CAPD library. Below, we provide links with corresponding requirements and instructions


The instruction for the CAPD library is available here .


The instruction for the CAPD library here.

Running instructions

where "input data file name" is the input data file name.

Input file structure

Refer the paper for the exact meaning of the input parameters. All the numbers should be entered explicitly, using the exponential notation, for instance 1e-02 is allowed. Note that only reasonable values should be used, refer Section 7 in the article for the example sets of parameters for which the algorithm completes successfully. For certain values a blow up during the integration process may occur, if so, a proper message is being outputted. More specific technical parameters can be changed by editing the config.h file and recompiling the program.

The output

The program saves the output data from the proofs into four output files. When the proof is complete four files appear in the bin directory. The files are as follows


This program is an open research software dedicated for performing computer assisted proof
Copyright (C) 2010-2013 Jacek Cyranka

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program. If not, see .

Please consult the webpage,
or contact me on jcyranka (at) for further details.