Theta method
= Theta method
{title2=$y_{n+1}-y_n=h[(1-a)f(y_n)+af(y_{n+1})]$}
This one-step family interpolates between the <Forward Euler method> at $a=0$, the <trapezoidal rule> at $a=1/2$, and the <Backward Euler method> at $a=1$. Its <stability function> is $R(z)=[1+(1-a)z]/[1-az]$. It is first order except at one half, where it is second order. Applying it to spatial diffusion gives the <theta diffusion stability criterion>.