# Finite difference method

1. Sep 8, 2009

### squenshl

How do I use the finite difference method with M = N = 20 to obtain a plot of the solution of

$$\nabla$$2u = 1, 0 < x < 1, 0 < y < 1,
u(x,0) = x(1-x), u(x,1) = x(1-x), 0 $$\leq$$ y $$\leq$$ 1,
u(0,y) = 0, u(1,y) = 0, 0 $$\leq$$ y $$\leq$$ 1.

2. Sep 9, 2009

### HallsofIvy

Staff Emeritus
Okay, what have you done on this? In particular, what would [itex]\nabla^2 u= 1[/math] look like in terms of this mesh?

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