ODE Solver

Features

Can solve systems of ordinary differential equation by using methods:

• Runge-Kutta fourth order method
• Adams extrapolation n-th order
• Adams interpolation n-th order
• Rosenbrock method for autonomous systems
• Predictor-Corrector method using Adams extrapolation and interpolation methods

How to use

Create ODE using std::function and create context:

std::function<std::vector<double>(double t, std::vector<double> x)> f = 
        [](double t, std::vector<double> x) -> std::vector<double>{
    std::vector<double> res(x.size());

    /*
     * Your system. For example:
     */
    
    res[0] = 10.0 * (x[1] - x[0]);
    res[1] = x[0] * (28.0 - x[2]) - x[1];
    res[2] = x[0] * x[1] - 8.0 * x[2] / 3.0;

    return res;
};



Context context = Context(f)

Then set the initial values, start and begin of integration and other parameters.

context.x_0 = {10, 10, 10};
context.t_begin = 0.0;
context.t_end = 100.0;
context.h = 5e-5; // Integration step
context.adams_order = 10; // Order of Adams methods

Then you can create instance of ODESolver:

ODESolver odeSolver = ODESolver(context);

Run integration by one of the methods: odeSolver.rk(), odeSolver.ae(), odeSolver.ai(). Then retrieve results from odeSolver.Results:

odeSolver.ae();

std::ofstream ae("ae.dat");

for (auto &step: odeSolver.Result)
{
    auto [ t, x ] = step;

    ae << std::fixed << std::setprecision(10) << t << " ";

    for (auto &item: x)
    {
        ae << item << " ";
    }

    ae << std::endl;
}

ae.close();

odeSolver.Result has type of std::vector<std::tuple<double, std::vector<double>>>.

How to compile and run test

Use Makefile by running:

make run

Results will be stored in ae.dat, ai.dat, rk.dat, precor.dat, rosen.dat. Plot them using:

gnuplot plot.plt