r/DifferentialEquations

Hi everyone,

I recently implemented the Runge–Kutta Fourth Order (RK4) method in C++ to solve the second-order differential equation

ax¨+bx˙+cx=0

The tutorial covers:

• Converting a second-order ODE into two first-order equations
• Implementing the RK4 algorithm in C++
• Writing simulation data to a .dat file
• Plotting Position vs Time and Velocity vs Time using GNU Plot

The goal was to make the implementation easy to understand for beginners and engineering students learning numerical methods.

I'd really appreciate any feedback on the implementation, coding style, or explanation. Suggestions for future C++ or numerical methods tutorials are always welcome.

If you find the tutorial helpful, please consider liking the video, sharing it with others who might benefit, and subscribing to the channel. Your support helps me create more tutorials on C++, Numerical Methods, Engineering Simulations, and GNU Plot.

Thank you for your support! 🚀

I've been learning numerical methods in C++ and created a tutorial showing how to solve a second-order differential equation using Euler integration and visualize the results with GNU Plot.

The equation I solve is:

aẍ + bẋ + cx = 0

I'm interested in hearing how others would approach this. Would you use Euler for teaching purposes, or would you start directly with RK4? Any suggestions or feedback are welcome.