Thread: Euler's method

The question goes...

Implement Euler's method in order to find a numerical solution of the equation

which satisfies

integrate over the domain , choosing suffiecently small step length.

Then I've gotta plot a graph on this program, which I'll be able to do if I had a clue how to do the question can anyone help?

Originally Posted by chella182

The question goes...

Implement Euler's method in order to find a numerical solution of the equation

which satisfies

integrate over the domain , choosing suffiecently small step length.

Then I've gotta plot a graph on this program, which I'll be able to do if I had a clue how to do the question can anyone help?

Haha. You must do Maths at Newcastle, aye?

The same as Matt.

I had to help him with it too :P.

Euler's method says that, given a step size h, and a differential equation then the solution to a differential equation is given by:



And that



So for you, your equations would be:





So your program should look something like this:

Code:

set x(1) = 0
set y(1) = -1
set h = 0.01

for k = 2 to 501 in steps of 1
     y(k) = y(k-1)+h*((y(k-1))^2-2*(x(k-1))*(y(k-1))+1+(x(k-1))^2);
     x(k) = x(k-1)+h;
end

plot(x,y)

Of course, I'm fairly sure you guys use maple, whereas I am more conversant in MatLab, so I can't give the program to you in Maple!

However, in matlab, it looks like this:

Code:

x(1) = 0;
y(1) = -1;
h= 0.01;

for i = 2:1:501;
     y(i) = y(i-1)+h*((y(i-1))^2-2*(x(i-1))*(y(i-1))+1+(x(i-1))^2);
 x(i) = x(i-1)+h;
end

plot(x,y,'r')

If I'm talking out of context here, you may be better to talk to Matt. He uses this forum, goes by the name Mitch something! He'll know.

I do indeed & I know Matthew

I don't remember doing Euler's method at all this semester so it confused me when it came up. Thanks though