Odes-NG

C++ library of (Ordinary) Differential Equations solvers, with routines adapted to Parabolic Equations.

(Why NG? because it is a New Generation of solvers).

This library contains:

1. optimized rewriting of classical stiff ODES solvers.

2. specialized versions of stabilized explicit solvers, mainly for large systems resulting from parabolic PDEs.

Stabilized explicit solvers (Rock*) are multi-threaded (openmp).

It is yet experimental !

Numerical Methods:

• Radau5-NG : rewriting of the classical Radau5 code (by Hairer and Wanner).

• Rock4-NG : rewriting of the code of A. Abdulle, with less memory copies.

• Rock4-L : specialization of Rock4 for linear problems.

• Rodas-NG : rewriting of the code Rodas (by Hairer and Wanner).

• SDIRKL : SDIRK methods, for linear problems.

• SymplectikRK : Gaussian symplectic methods.

We hope to add at least 2 other methods in the (near?) future: a rewritten version of Rock2, and a specialization of Rock2 for linear problems.

Structure:

• Odes-NG/common/include/: contains parts of code common to all integrators.

• For each integrator, the directory contains:

  • include/ : the core integrator.
  • test/ : examples, and some documentation.
  • An optional sage/ sub-directory contains SageMath material used to build the codes.

Concept:

User provides a C++ class which should completely describe the problem:

• RHS (and if necessary Jacobian of RHS).
• Size (number of equations).
• Some operators if necessary.
• Constants.
• ...

This allow to inline functions in the case of a rather simple RHS.

The original codes for Radau5, Rodas, Rock2 and Rock4 can be found at https://www.unige.ch/~hairer/software.html

Doxygen documentation:

Just do:

 doxygen Doxyfile 

Documentation (html and latex) goes in Doc/

The main page of the html documentation explains how to use these codes.

How to build and run the tests:

cd Radau5-NG   (or Rock4-L, Rock4-NG, Rodas-NG and so on)
cd test
mkdir Build
cd Build
export CXX=your_compiler (with your compiler = g++ or icc or clang++; default:g++)
cmake ..
make
./run

Note that:

Odes-NG introduces the namespace odes.

References:

To learn about Ordinary Differential Equations solvers, you should read the bible:

• Solving Ordinary Differential Equations I, by Hairer, Nørsett,, Wanner,
• Solving Ordinary Differential Equations II Stiff and Differential-Algebraic Problems by Hairer and Wanner,
• Geometric Numerical Integration by Hairer, Lubich and Wanner.

About Rock methods, you can also read this paper.