[Boost-users] Math and numerics: Odeint - problem with adaptive step size

Subject: [Boost-users] Math and numerics: Odeint - problem with adaptive step size
From: William Heitler (wjh_at_[hidden])
Date: 2018-02-20 11:15:20

Hello,

I'm a moderately experienced C++ programmer using Visual Studio 2017, but I'm new to using the boost odeint library.
I'm trying to integrate the Hodgkin-Huxley  equations, which are a set of ODEs that describe the generation of nerve impulse. The output should be a time-series waveform which is mainly flat but with occasional spikes in it.
I have a functor HH which works fine with a standard fixed-step Runge-Kutta routine

    runge_kutta4< state_type > stepper;
    integrate_const(stepper, HH, x, 0.0, 20.0, 0.04,trace_observer());

This code produces exactly the right waveform

However, I would like to use an adaptive step size because the waveform is pretty flat between the spikes. I tried the following:

    integrate_adaptive(make_dense_output(1.0e-6, 1.0e-6, runge_kutta_dopri5< state_type >()), hh, x, 0.0, 10.0, 0.04, trace_observer());

This works up to about the peak of the first spike, but then crashes with the error message:
    Debug Assertion Failed!

    ...

    Expression: vector iterator not incrementable

It dies in the Visual Studio vector library code

    _Vector_const_iterator& operator++()

in a call from boost::norm_inf where iterator first1 reports as

    first1    {2.105352686232e-314#DEN}    std::_Vector_const_iterator<std::_Vector_val<std::_Simple_types<double> > >

I certainly don't understand how the boost code works under the hood, but I wondered if anyone could suggest a change in my calling code that might make it work? I have hand-crafted some adaptive step size code which works OK (and does run faster than the fixed step size), but it is a bit of a kludge and I would rather use code developed by people who actually understand the maths.

For reasons of brevity I haven't put the HH code in this message, but could do if it would help.

Thanks for any help

Dr W J Heitler
School of Biology
University of St Andrews
01334 463490
www.st-andrews.ac.uk/~wjh<http://www.st-andrews.ac.uk/~wjh>