certaingemstone/simplerk4

An implementation of a 4th-order Runge-Kutta numerical solver for systems of 1st order differential equations.

SimpleRK4

C++ implementation of a 4th-order Runge-Kutta numerical solver for systems of 1st order differential equations.

Description

Accepts arbitrary number and type of equations as input, returns vector of variable values over time; useful for state-space representations of dynamical systems.

How to use

After including the files (rk4.h and the accompanying implementations in rk4.cpp), declare your differential equations as functions accepting a vector<double> (state of the system) and a double (time), while returning a double. For example,

    double dxdt(std::vector<double> state, double time) {
        double derivative;
        //some code here to calculate the derivative of x given the state and/or time
        return derivative;
    }

Then in the main function, create a vector of function pointers to store your derivatives, like

    std::vector<double (*)(std::vector<double>, double)> diffeqs;
    diffeqs.push_back(dxdt);
    diffeqs.push_back(dydt);

Also create a vector<double> to store your initial state.

Now, instantiate an rk4::rk4Solve with your initial state vector, starting time, size of time step, and derivative functions (note the number of state variables and number of equations governing them must match):

    rk4::rk4Solve Solver(stateInitial, 0.0, 0.02, diffeqs);

Calling iterate() will move the system forward by one timestep, returning a vector of the new state variables.

See demo code for details, in this case solving the equations of motion of a double pendulum.