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}) $