A modified form of [[Euler's Method]] taking account of [[Partial Derivative|partial derivatives]] to solve [[Ordinary Differential Equations]].
$\large
z_{i+1} =
z_{i} + hf(t_{i},z_{i})
+ \frac{h^{2}}{2}
\partial_{t}f(t_{i}z_{i})
+ \frac{h^{2}}{2}
\partial_{y}f(t_{i}z_{i})
f(t_{i},z_{i})
$