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Crank-Nicholson is usually used for linear ODE but can also be extended to a nonlinear ODE $$\dot z = f(z)$$ like so: $$\frac{z_{n + 1} - z_n}{\delta t} = \frac{f(z_{n + 1}) + f(z_n)}{2}.$$ Another similar alternative is the implicit midpoint rule: $$\frac{z_{n + 1} - z_n}{\delta t} = f\left(\frac{z_{n + 1} + z_n}{2}\right).$$ The Crank-Nicholson and ...


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