trying to use heun's method to solve an ode

I am trying for days to solve an ode using heun's method for a project but i always keep getting an error message!!!this is what I tried :

f = @(t,y)(m*yn' + c*yn + k*yo - F0*sin(w*t));

a = 0;

b = 10;

n = 100;

h = (b-a)/n;

T = a:h:b;

F0 = 0;

w = 0;

m = 4;

k = 10;

c = 0.2;

y0 = 4;

[t,y] = myHeun(y0,a,b,f,n);

plot(t,y,'k')

[Ankit]

could you post the screenshot of your error message?

[Anas Gharsa]

this is what i get

Unrecognized function or variable 'yn'.

Error in ex7>@(t,y)(m*yn'+c*yn+k*yo-F0*sin(w*t)) (line 3)

f = @(t,y)(m*yn' + c*yn + k*yo - F0*sin(w*t));

Error in myHeun (line 10)

fi=feval(f,t(i),u(i)); %evaluation of f at t_i, u_i

Error in ex7 (line 19)

[t,y] = myHeun(y0,a,b,f,n);

[Anas Gharsa]

and when i set yn = y'; i get message like this

Error in ex7 (line 1)

yn = y';

[Anas Gharsa]

I even tried something like this :

f = @(t,y)(m*yn' + c*yn + k*yo - F0*sin(w*t));

a = 0;

b = 10;

n = 100;

h = (b-a)/n;

T = a:h:b;

F0 = 0;

w = 0;

m = 4;

k = 10;

c = 0.2;

y0 = 4;

h=(b-a)/n; %h=(b-a)/n

t=a:h:b;

u=y0*ones(1,n+1); %initial condition

for i=1:n

fi=feval(f,t(i),u(i)); %evaluation of f at t_i, u_i

u0=u(i)+h*fi; %application of Euler method to obtain u_{i+1}^0

u(i+1)=u(i)+h*(fi+feval(f,t(i+1),u0))/2; %application of Heun method

end

plot(t,y,'k')

and i get this error message:

Error in ex7>@(t,y)(m*yn'+c*yn+k*yo-F0*sin(w*t)) (line 3)

f = @(t,y)(m*yn' + c*yn + k*yo - F0*sin(w*t));

Error in ex7 (line 21)

fi=feval(f,t(i),u(i)); %evaluation of f at t_i, u_i

[Torsten]

What is yo ?

Answer 1

[VBBV]

a = 0;
b = 10;
n = 100;
h = (b-a)/n;
% T = a:h:b;
F0 = 0;
w = 0;
m = 4;
k = 10;
c = 0.2;
y0 = 4;
h=(b-a)/n;                                                     %h=(b-a)/n
t=a:h:b;
u=y0*ones(1,n+1);       
f = @(t,y)(m*y + c*y + k*y0 - F0*sin(w*t));%initial condition
for i=1:n-1  
    fi=feval(f,t(i),u(i));                                      %evaluation of f at t_i, u_i
    u0=u(i)+h*fi;                                              %application of Euler method to obtain u_{i+1}^0
    u(i+1)=u(i)+h*(fi+feval(f,t(i+1),u0))/2;        %application of Heun method
end
plot(t,u,'k')

[VBBV]

Check the steps of your algorithm,

[Torsten]

@VBBV

The function must read

f=@(t,y)(F0*sin(w*t)-(c*y+k*yo))/m

(whether yo is y0 only the OP knows)

[Anas Gharsa]

the real function is of second degree, i have to trasforme it to the first degree so i can solve it with the heun's method so yo actually is y and yn=y'

[Torsten]

And yn' is y'' ?

Then the solution given is of course wrong.

Why don't you clarify such things and let VBBV waste his time ?

[Anas Gharsa]

yes!! yn' si y"!! sorry about that i didn't know

[Anas Gharsa]

so what is kind of problem here ??? because i am not understanding anything anymore!!

[Torsten]

You wrote you want to learn Matlab, and this is fine.

But since you got your problems as exercises for your homework, you should be able to state them properly.

And everybody in the forum is willing to help if you show that you spent some effort to solve the problem on your own. But did you really spend this effort ? Since the Heun program can't be written on your own if you don't know how to use it.

[Anas Gharsa]

Dear Torsten, you got right to say that since you really don't know how much time i spend on this. I am not asking to risolve the exercises for me I am just asking some advices that would help me and may be guidance to the right direction!! and like i said it befor i am new to matlab and i am doing my best to learn it !! and for the Heun algorithm i did what i could after reading thounsands of pages that speaks of numerical solutions and reading many others scripts!! you can say everything you want but you can't tell me that i did nothing to try it by my self

by the way thank you for trying to help and thank you so much VBBV