Euler's method for 2nd order ODE

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oday hazaimah 2019-7-2

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https://ww2.mathworks.cn/matlabcentral/answers/469936-euler-s-method-for-2nd-order-ode

评论： Geoff Hayes 2019-7-5

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]

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oday hazaimah 2019-7-4

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 2019-7-5

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?

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回答（1 个）

Vaibhav Tomar 2019-7-4

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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) 