Comparing Methods for Initial Value Problem

[evinda]

And what if we write these two function into one?

I mean like that:

function [ ] = ex(N) 
h=1/N;
A=[-5 -2;-2 -100]; 
%trapezoid_method  
y=[1;1];
t2=[0];
y2=[y];
for (i=1:N)
      y=(eye(2)+h*A+h^2/2*A^2)*y;
      t2=[t2, i*h];
      y2=[y2, y];
end 
%euler_method  
y=[1;1];
t3=[0];
y3=[y];
for (i=1:N)
    y=inv(eye(2)-h*A)*y;
    t3=[t3, i*h];
    y3=[y3, y];
end 
plot(t2, y2(1,:).^2+y2(2,:).^2, 'y', t3, y3(1,:).^2+y3(2,:).^2, 'b'); 
end

So that the variables are known, does the function have to return these? Or how can we fix the error that we get, that the variable are not known? I splitted the two functions into two files, the following:

function [ ] = euler(N) 
h=1/N;
A=[-5 -2;-2 -100]; 
%trapezoid_method  
%euler_method  
y=[1;1];
t3=[0];
y3=[y];
for (i=1:N)
    y=inv(eye(2)-h*A)*y;
    t3=[t3, i*h];
    y3=[y3, y];
end 
end

function [ ] = trapezoid(N) 
h=1/N;
A=[-5 -2;-2 -100]; 
%trapezoid_method  
y=[1;1];
t2=[0];
y2=[y];
for (i=1:N)
      y=(eye(2)+h*A+h^2/2*A^2)*y;
      t2=[t2, i*h];
      y2=[y2, y];
end 
end

Then in the command line I wrote the following commands:
octave:1> trapezoid(100)
octave:2> euler(100)
octave:3> plot(t2, y2(1,: ).^2+y2(2,: ).^2, 'y', t3, y3(1,: ).^2+y3(2,: ).^2, 'b');

but I get again "error: 't2' undefined near line 1 column 6". What am I doing wrong? (Thinking)

Here's how it looks like at me:View attachment 9069

 

[I like Serena]

And what if we write these two function into one?

I mean like that:

So that the variables are known, does the function have to return these? Or how can we fix the error that we get, that the variable are not known?

That should work yes.
Does it? (Thinking)

I splitted the two functions into two files, the following:

Then in the command line I wrote the following commands:
octave:1> trapezoid(100)
octave:2> euler(100)
octave:3> plot(t2, y2(1,: ).^2+y2(2,: ).^2, 'y', t3, y3(1,: ).^2+y3(2,: ).^2, 'b');

but I get again "error: 't2' undefined near line 1 column 6". What am I doing wrong? (Thinking)

Here's how it looks like at me:

Now we do not get the error that there is something wrong with the script any more. Good! (Happy)

The variables still need to be returned though.
We can do that with:
[M] function [t3, y3] = euler(N)
...[/M]
and:
[M]function [t2, y2] = trapezoid(N)
...[/M]
and:
[M]octave:1> [t2, y2] = trapezoid(100)
octave:2> [t3, y3] = euler(100)
octave:3> plot(t2, y2(1,: ).^2+y2(2,: ).^2, 'y', t3, y3(1,: ).^2+y3(2,: ).^2, 'b'); [/M]
(Emo)

 

[evinda]

The variables still need to be returned though.
We can do that with:
[M] function [t3, y3] = euler(N)
...[/M]
and:
[M]function [t2, y2] = trapezoid(N)
...[/M]
and:
[M]octave:1> [t2, y2] = trapezoid(100)
octave:2> [t3, y3] = euler(100)
octave:3> plot(t2, y2(1,: ).^2+y2(2,: ).^2, 'y', t3, y3(1,: ).^2+y3(2,: ).^2, 'b'); [/M]
(Emo)

I tried it like that. The command "[t2, y2] = trapezoid(100)" works. But the command "[t3, y3] = euler(100)" seems not to work, I get the following:View attachment 9070(Thinking)

 

[I like Serena]

I tried it like that. The command "[t2, y2] = trapezoid(100)" works. But the command "[t3, y3] = euler(100)" seems not to work, I get the following:

It seems to work for me:

View attachment 9071

(Wasntme)