The equestion you wrote is first order Euler's method for no free charge case.
You can modify it to second order differential method (use potential V)
\frac{\partial^2 V}{\partial x^2}+\frac{\partial^2 V}{\partial y^2}+\frac{\partial^2 V}{\partial z^2}=0
and use relazation method (change to boundary value problem) to find the solution for V. Then calculate Ex,Ey,Ez from V.