solving a function with indecis

I want to compute a function f, for example, f=sin(t*x) with this recursive algorithm.

      h=.01;y0=1;t0=0;
for i=0:10
   t(i+1)=ti+h;
   c1=func(ti, yi);
   c2=func(ti+(h/2),yi+(h/2)*c1);
   y(i+1)=yi+h/6*(c1+2*c2);

end

And I defined function func in the separate file. This loop doesn't run from the first line. I don't know what is the problem. First I want to know this way of writing indices is correct? second, how can I get the value of y at the end? Could you please help me with this? Thank you

[Ameer Hamza]

what are yi, c1 and c2. Are c1 and and c2 even defined. Also, do you mean y(i) instead of yi.

[RSHU FA]

Thank you for your comment. You mean I have to write y_(i+1)as yi+1? without parenthesis? These indices don't produce during the for loop?

Answer 1

[Torsten]

All variables must be defined before you use them.

Look at the first line of your loop: here, yi, c1 and c2 are not yet defined to calculate y(2).

Best wishes

Torsten.

[RSHU FA]

Thank you for your answer. These indices don't produce during the for loop? I started i=0 instead 1.

[Torsten]

yi remains yi - i=0 is not substituted here.

Furthermore, c1 and c2 are not yet defined when you try to evaluate y(i+1).

[RSHU FA]

Excuse me I don't get it! I have y0 and t0. then for c1=func(t0,y0)for first time and again second line,... Besides, defining index in this way is correct? t(i+1) or ti+1?

[Torsten]

h=.01;
t(1)=0;
y(1)=1;
for i=1:10
   c1=func(t(i),y(i));
   c2=func(t(i) + h/2,y(i) + h/2*c1);
   y(i+1) = y(i) + h/6*(c1+2*c2);
   t(i+1) = t(i) + h;
end

[RSHU FA]

Thank for your help, I really appreciate that. Now to see final y, I have to use which one? fprint, display,...? All these get me an error!

[Torsten]

plot(t,y) 

after the loop.

[RSHU FA]

I got:

   Error using plot
Vectors must be the same length.

[Torsten]

Please show your code.

[Torsten]

t(1)=0;
h=.1;
y(1)=3;
for i=1:100
t(i+1)=t(i) + h;
 c1=functionq1(t(i),y(i));
 c2=functionq1(t(i)+h/2,y(i) +h/2*c1);
 c3=functionq1(t(i)+h/2,y(i) +h/2*c2);
 c4=functionq1(t(i) +h, y(i) +h*c3);

     y(i+1)=y(i) + h/6*(c1+2*c2+2*c3+c4);
  end
  tspan=0:0.1:10;
  y0=3;
  [X,Y]=ode45(@funcq1, tspan, y0);
  plot(X,Y,t,y);

[RSHU FA]

Thank you a lot.I couldn't even thank you. The problem was only because of i should be from 1 to 100!interestin!

Now how can I compare the maximum difference between this two? with max(Y-y) I don't get the right result

[Torsten]

with max(Y-y) I don't get the right result

Why ? What's the problem with

max(abs(Y(:,1)-y(:))) 

?

[RSHU FA]

with max(Y-y) I get two many numbers like:

    Columns 1 through 19

   56.1546   56.0333   55.8888   55.7191   55.5210   55.2904   ..   

Columns 20 through 38

   43.7418   42.1609   40.5228   38.7424   36.9352   35.2361   ..   

with max(abs(Y(:,1)-y(:))) I get one number, it's OK. But w.r.t the figure I think the bigger difference happens in the maximum of this function but max(Y)-max(y) is not equal to max(Y-y). how can I get the t component for max(y) and max(Y)? Maybe because y is w.r.t t and Y is w.r.t X.