Runge's phenomenon: when equally spaced nodes betray you. Increase the degree of your interpolating polynomial, and instead of converging, it explodes near the endpoints of [-1,1]. The culprit isn't the function's real-line behaviour — it's complex singularities hiding just off the axis, silently poisoning the convergence that equally spaced nodes can never achieve. Thankfully chebyshev interpolation points save the day!

Numerical Methods Simplified – Runge-Kutta 2nd Order Method Formulas

Numerical Methods Simplified – Runge-Kutta (4th Order) Method Formulas