An improvement to the Forward Euler method is Heun’s method, a
“predictor-corrector” approach that uses the predicted values at
the next time step to create a second improved (“corrected”)
approximation.
Given the first order ODE y′ =
f (x, y), and a point on the solution
curve (xn , yn), we want
to estimate the next point at a step size h later. We make
a first prediction of the next value, y*, using the
forward Euler approach:
xn+1 = ...