(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

We wanna solve the equation

[tex]u_{xx}(x,y) + u_{yy}(x,y) = xu(x,y) [/tex]

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 [tex]u_{1,1}, u_{2,1}, u_{1,2}[/tex] and [tex]u_{2,2}[/tex]

2. The attempt at a solution

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

-4[tex]u_{1,1}[/tex] + [tex]u_{2,1}[/tex] + [tex]u_{1,2}[/tex] = -x + x[tex]u_{1,1}[/tex]

This can be written

-13/3[tex]u_{1,1}[/tex] + [tex]u_{2,1}[/tex] + [tex]u_{1,2}[/tex] = -1/3

The correct equation for this point is

-109[tex]u_{1,1}[/tex] + 27[tex]u_{2,1}[/tex] + 27[tex]u_{1,2}[/tex] = -9

What is wrong?

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# Homework Help: Dirichlet problem

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