Runge-Kutta Numerical Solutions to Differential Equations
Mathematical Computation

Runge-Kutta Numerical Solutions to Differential Equations

This is an implementation of the RK4 Method to solving differential equations implemented using C++.

  • Date: 23 Mar 2020
  • Role: Hobby Developer

ARK (Angel’s Runge-Kutta) is a personal project / C++ macro I wrote to numerically solve first and second order differential equations using the Runge-Kutta Method. This algorithm is implemented using C++, which I chose for its speed and malleability. Examples of ARK solving the exponential ODE and the Simple Harmonic Oscillator ODE can be seen below!

The Exponential Function differential equation evaluated using RK4 The Simple Harmonic Osciallator differential equation evaluated using RK4 The Sinc Function differential equation evaluated using RK4

I also wrote a python file to plot the analytic solutions of these ODEs against the numerical solutions from ARK. This can be found as rk4_analysis.py in both folders. You may also find a file called derivatives.cpp which calculates the value of a derivative at a certain point.

This personal project is in active development, so please feel free to submit issues or a pull request!

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