How-to: solve a simple ODE#

Note

You can also see Very first steps with Lorenz system tutorial.

We would like to solve the following equation

\[\dot{y} = -y,\qquad y(0) = 1\]

We first define the function \(f:(t,y)\mapsto f(t, y) = -y\), in ponio we define this function as f(double t, double y, double& dy), where the current state y can be capture by value, reference or constant reference.

19    auto f = []( double /* t */, double y, double& dy )
20    {
21        dy = -y;
22    };

We also define initial condition and time step:

24    double const y0 = 1.0;
25    double const dt = 0.1;

Next we solve this equation with explicit Euler method defines in ponio as ponio::runge_kutta::euler.

27    ponio::solve( f, ponio::runge_kutta::euler(), y0, { 0., 2.0 }, dt, "how_to_solve_exp.txt"_fobs );

In this line we call ponio::solve() function, with a observer::file_observer to store the output in how_to_solve_exp.txt text file.

Note

To use the _fobs literal you need to using the correct namespace

    using namespace ponio::observer; // to use _fobs litteral

See also

The full example can be found in how_to_solve_exp.cpp.

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