Hi, ----- Original Message ----- From: "Karsten Ahnert" <karsten.ahnert@gmx.de> To: <boost@lists.boost.org> Sent: Sunday, December 13, 2009 4:02 PM Subject: [boost] library proposal: odeint

Hi,

I am new on this list and want to start a discussion if a library for solving ordinary differential equations (ODEs) would fit into boost.

We are developing a lib - odeint - for such problems. odeint can be found in the sandbox: https://boost.org/svn/boost/sandbox/odeint, but the current stage is far away from being ready for release or submission.

If you don't reach to get the link, try with http://svn.boost.org/svn/boost/sandbox/odeint/

ODEs are usually solved iteratively. Therefore, we have introduced two stepper concepts, one for steppers with- and one for steppers without error estimation. At the moment some explicit solvers are implemented: Euler, RK4, Cash Karp, RK78,midpoint and Burlisch-Stoer.

Here are some examples:

typedef std::tr1::array< double , 3 > state_type;

// define the ODE void lorenz( state_type &x , state_type &dxdt , double t ) { const double sigma = 10.0 , R = 28.0 , b = 8.0 / 3.0 dxdt[0] = sigma * ( x[1] - x[0] ); dxdt[1] = R * x[0] - x[1] - x[0] * x[2]; dxdt[2] = x[0]*x[1] - b * x[2]; }

state_type x = {{ 1.0 , 0.0 , 0.0 }}; ode_step_euler< state_type > stepper; double t = 0.0;

// iterate the ODE by hand with constant stepsize for( size_t oi=0 ; oi<10000 ; ++oi,t+=dt ) stepper.next_step( lorenz , x , t , 0.01 );

// integrate the ODE with constant stepsize // from t = 0.0 to t = 100.0 with dt = 0.01 // and write t and x[0] to cout integrate_const( rk4 , lorenz , 0.0 , 0.01 , x , 100.0 , cout << _1 << tab << _2[0] << "\n" );

// stepsize controller for rk5 cash-karp controlled_stepper_standard< stepper_rk5_ck< state_type > > rk5_controlled( rk5 , eps_abs, eps_rel, 1.0, 1.0);

// solve the ODE with an adaptive stepsize controller size_t steps = integrate_adaptive( controlled_rk5, lorenz, x, 0.0, 10.0 , 0.01, cout << _1 << tab << _2[0] << "\n" );

Please, could you post in this list when some documentation will be available? I will add a link on the Libraries Under Construction wiki as soon as some documentation is available on line(http://svn.boost.org/trac/boost/wiki/LibrariesUnderConstruction) Best, Vicente

I am new on this list and want to start a discussion if a library for solving ordinary differential equations (ODEs) would fit into boost.

...

ODEs are usually solved iteratively. Therefore, we have introduced two stepper concepts, one for steppers with- and one for steppers without error estimation. At the moment some explicit solvers are implemented: Euler, RK4, Cash Karp, RK78,midpoint and Burlisch-Stoer.

Without meaning to be off putting, have you looked at pure C libraries like the GNU Scientific Library to see if they contain what you need? GSL's routines [1] are quite good and cover a large number of the features you mention. You might save yourself the trouble of writing and testing everything and instead only need to wrap the GSL routines with your C++ interface. If GSL doesn't contain exactly what you want (RK78 comes to mind), you'll probably find the GSL ODE framework quite useful for writing the stepper you want. If you choose to submit it there, then everyone in C- and C++-land benefits from the submission. - Rhys [1] http://www.gnu.org/software/gsl/manual/html_node/Ordinary-Differential-Equat...