# Dirichlet problem

1. Nov 27, 2008

### leopard

1. The problem statement, all variables and given/known data

We wanna solve the equation

$$u_{xx}(x,y) + u_{yy}(x,y) = xu(x,y)$$

on the square [0,1]x[0,1] with boundary conditions

u(x,0) = x
u(x,1) = x
u(0,y) = 0
u(1,y) = 1

Let h = 1/3 be the mesh. Set up a system of equations for $$u_{1,1}, u_{2,1}, u_{1,2}$$ and $$u_{2,2}$$

2. The attempt at a solution

First point (1/3, 1/3):

-4$$u_{1,1}$$ + $$u_{2,1}$$ + $$u_{1,2}$$ = -x + x$$u_{1,1}$$

This can be written

-13/3$$u_{1,1}$$ + $$u_{2,1}$$ + $$u_{1,2}$$ = -1/3

The correct equation for this point is

-109$$u_{1,1}$$ + 27$$u_{2,1}$$ + 27$$u_{1,2}$$ = -9

What is wrong?

Last edited: Nov 27, 2008