How would I improve my euler code?

How can i improve my euler code? Code is attached ... I believe i have to improve it by using trapezoids instead of rectangles..How do i do this ? Can someone help

Answer 1

[Jim Riggs]

For trapezoidal integration, you use the average of two consecutive evaluations. This could be done by simply adding one line of code after the Euler calculation;

 y(:,k+1) = (y(:,k+1) + y(:,k))*h/2

[Raiven Balderas]

so i add your suggestion directly below "y(:,k+1)=y(:,k)+h*func(t(k),y(:,k)); " ?

[Jim Riggs]

Perhaps this will be more clear:

 A = func(t(k),  y(:,k)  );
 B = func(t(k+1),y(:,k+1));
 y(:,k+1) = y(:,k) + (A + B) * h/2;

Compare this with the Euler method:

 A = func(t(k),  y(:,k)  );
 y(:,k+1) = y(:,k) + A * h;