Backward Euler Method

[mathmari]

Hi!!! I need some help...
I want to write a code in matlab for the backward euler method.
How can I solve the equation to determine y^(n+1)??? Are newton's method, fixed point iteration, fsolve, fzero equal???

[mathmari]

To use Newton's method, do i have to write:

for i=1:n
y(n+1)=y(n)-(g(y(n))/dg(y(n));

where g=y(n+1)-y(n)-h*f(t(n+1),y(n+1)) ???

[elfmotat]

For the backward Euler's method, you could use something like the following:

 

clc;
clear;

ti=0;
tf=10;
n=5000;
h=(tf-ti)/n;
t(1)=ti;
y(1)=1;

for i=1:n
dydt=sin(t(i));
t(i+1)=t(i)+h;
y(i+1)=y(i)+h*dydt;
end;

plot(t,y)

 

 

I used dy/dt=sin(t) as an example function. To make it go backwards, all you have to do is make tf<ti, so that h becomes negative.

Edited April 27, 2013 by elfmotat

[mathmari]

Ok... Thank you very much!!!!