02 · Numerical Methods
Investigations of Variations on a Theme of Euler
Using Euler, backward Euler, Heun's method, and RK4 to solve initial-value problems for ordinary differential equations.
Four methods, one family of initial-value problems, and the question of what accuracy actually costs. Forward Euler is the cheapest and the least forgiving. Backward Euler trades an implicit solve for stability. Heun’s method and RK4 buy accuracy per step with extra evaluations of the derivative.
The interest is in where each one breaks: stiff problems, long integration windows, and the point at which a smaller step size stops helping.
