# Welcome to VERICOMP

VERICOMP is a system for comparing and testing *verified solvers* for initial value problems. Verified solvers generate numerical sets that are mathematically proved to contain exact solutions. More information about verified algorithms and solvers is in the Links section of this site.

## Our motivation

Obtaining *verified solutions* to IVPs for ordinary differential equations is *important in many application areas*, such as biomechanics or automatic control. Test sets and comparison systems for floating-point based solvers turned out to be very useful (Test set, ODELab). Our hope is that *a similar framework for verified solvers* would promote their use.

## VERICOMP is different

Verified solvers have to be *compared differently* from their floating-point analogs. The main reason is that they perform unequally on problems with and without uncertainty. In either case, the result is an interval with a non-zero width, and it can happen, due to dependency and wrapping , that the considered solver does not reach the predefined integration time (possible break-down). Besides, the reliability of the result does not have to be assessed, because the obtained enclosures are mathematically proved to contain the true solution.

## Getting started

For some features of VERICOMP you need an *account*. This is a security issue for us and it makes keeping track of the comparison results easier for you, too.

**> Please register! <**

## What you can do on VERICOMP

Problems | Browse the problem database |

Add problem* | Add a new problem to the benchmark database |

Solvers | View available solvers |

Recommend | Get a solver recommendation for your problem |

* requires a registered user account

## Current comparison criteria

Our recommendations are based on benchmarks of specific test criteria.

C4 | Wall-clock time |

C5 | The relation of the user CPU time to the overestimation (e.g., the interval width) at the end of the test period of 1 second |

C6 | The break-down time and the width of the interval at that point. Here, we simulate until t=10 |

## Created statistics

Work in progress ...

ASCII files with solutions |

Work-precision diagrams (WPD) |

Tables with criterion data |

Solution plots and PDF description files |