Milstein method
= Milstein method
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For a scalar <stochastic differential equation>, the Milstein method adds the quadratic-variation correction
$$
X_{n+1}=X_n+a(X_n)\Delta t+\sigma(X_n)\Delta W_n
+\frac12\sigma(X_n)\sigma'(X_n)
\left((\Delta W_n)^2-\Delta t\right).
$$
Under standard smoothness assumptions it has <strong order of convergence> one and <weak order of convergence> one.