4th-order Runge-Kutta

The 4th-order Runge-Kutta method is a numerical technique used to solve differential equations, which describe how things change over time or space. It calculates the solution in small steps by estimating the slope (rate of change) at several points within each step. Specifically, it takes four evaluations of the derivative: at the beginning, two midpoints, and the end of the interval, then combines them with weighted averages. This approach provides a highly accurate estimate of the function's future value, balancing computational effort with precision, and is widely used in scientific and engineering applications for simulating dynamic systems.