## Euler's method for 2nd order ODE

### oday hazaimah (view profile)

on 2 Jul 2019
Latest activity Commented on by Geoff Hayes

### Geoff Hayes (view profile)

on 5 Jul 2019
I am trying to run a code for solving 2nd order ODE but I have no idea where is my mistake in the following code:
function f=f(t0,x0,y0,N)
h=0.01;
N=5;
t0=0;
x0=0;
y0=0;
H=zeros(1,N+1);
T=zeros(1,N+1);
X=zeros(1,N+1);
Y=zeros(1,N+1);
H(1)=h; T(1)=t0; X(1)=x0; Y(1)=y0;
for j=1:N
T(j+1)=T(j)+H(j);
X(j+1)=X(j)+H(j)*Y(j);
Y(j+1)=Y(j)+H(j)*ahat(T(j),X(j),Y(j));
H(j+1)=H(j)*(1-H(j));
end
plot [T X]
plot [T Y]

Geoff Hayes

### Geoff Hayes (view profile)

on 4 Jul 2019
no numbers come out...can you clarify where you are expecting to see numbers? In the console window? There are no fprintf's or any other code in your function to write data to the console so not sure what you are expecting to see....
oday hazaimah

### oday hazaimah (view profile)

on 4 Jul 2019
Geoff,
Usually after we run the code we see the results come out in the command window so I am expecting to see columns with the error to compare between the valuse and then see the graphes of the functions X,Y,T
Geoff Hayes

### Geoff Hayes (view profile)

on 5 Jul 2019
oday - since the code is not explicitly writing anything to the console and because all lines are terminated with a semi-colon, then you will not see any output. As for the error...which array/variable does that correspond to?

### Vaibhav Tomar (view profile)

on 4 Jul 2019

Can you please specify the values of T, Y and X. Without that it's difficult to say why the code is throwing errors. I'd suggest to look for an example for second order ODE algorithm.
You can try this alternate code:
% x1=y
%x2=dy
%then
%dx1=dy=x2
%dx2=d2y=-w^2*y=-w^2*x1
%save this function as yourfcn
function dx=yourfcn(t,x)
w=1
dx(1)=x(2)
dx(2)=-w^2*x(1)
%Then call the ode45 function
[t,x]=ode45(@yourfcn,[0,pi],[0 0])
%Then deduce y
y=x(:,1)

oday hazaimah

### oday hazaimah (view profile)

on 4 Jul 2019
what values? aren't these the initial values that we already used above in the code and then the for loop will continue afterwards ?