# Laplace numerical solution

1. Feb 9, 2009

### purejoker

hi there, im a bit stuck can someone help?

i have a 5 point grid
--_______v1
--_______|
--_______|
v3-------v0-------v4
--_______|
--_______|
--_______v2

--_______ used to postion the | (y-axis) the grid is a plus sign.

they are seprated by $$\delta$$x and $$\delta$$y

i've worked out upto the second differential:
(v3-v0/$$\delta$$x - v0-v4/$$\delta$$x) /$$\delta$$x + (v1-v0/$$\delta$$y - v0-v2/$$\delta$$y) /$$\delta$$y = 0

the problem is i dont know how to get to this stage:

v0 = 1/4 (v1+v2+v3+v4)