# Math Help - Backward Euler Method for 2x2 systems

1. ## Backward Euler Method for 2x2 systems

Hi!!!
I want to write a code in Matlab for the Backward Euler Method for 2x2 systems, using the fixed point iteration to find the yn+1.
y1n+1=y1n+h*f(tn+1,y1n+1,y2n+1) (1)
y2n+1=y2n+h*g(tn+1,y1n+1,y2n+1) (2)
Could you tell how I use the fixed point iteration??
At (1) the fixed point iteration will calculate y1n+1, y2n+1 will be calculated at (2) but it is already used in the equation (1) ...

2. ## Re: Backward Euler Method for 2x2 systems

The fixed point algorithm should be the same as the one for single equation but the iteration function function will be a 2*1.

w1=y1+h*f(t,y1,y2)
w2=y2+h*g(t,y1,y2)
w=[w1;w2]
the iteration equation then
while y-y_1<tol
y=w
end
the solutions are:
y1=y(1)
y2=y(2)

hope that helps!

3. ## Re: Backward Euler Method for 2x2 systems

Ok! Thank you!!!