MATLAB: Dealing with Subscript Error

errorsimpsonvariables

I'm trying to approximate the integral of a function using the composite Simpson's rule. This means I'll have to input a function, the maximum and minimum of the interval, and an number of integration nodes. Specifically, the exercise demands that I use the interval [0,10].
Now, I've written the code for the Simpson's rule, and it works. The problem is when I try to use an interval that starts with 0, like it happens in the exercise. For example, let's imagine I have this function:
x=1:100;
y(x)=x.^2;
plot(x,y(x));
When the Simpson rule calls for y(0), I get an error message indicating that the subscript must be a positive integer. Now, I understand why this must be. The variable x is defined as a vector, and there's no "0" subscript in that vector; it has to be 1, or 2,1, etc. But I need to be able to get a value for the function at 0 in order for the Simpson's rule to work. How can I circumvent this issue? Is there a way to define x so that y(x) can accept fractions, negative numbers or zero?
Here's my code for the CSR by the way:
function F=simpsonc(y,a,b,N)
h=(b-a)/N;           
f=zeros(N+1,1);      
f(1)=a;f(N+1)=b;y1=0;y2=0;  
for z=2:N
    f(z)=a+z*h;    
end
for z=2:(N/2);
    y2=y2+y(f(2*z-1));
end
for z=2:(N/2)-1;
    y1=y1+y(f(2*z));
end  
F=(h/3)*(y(a)+y(b)+4*y2+2*y1);
end

Best Answer

Matlab won't let you use zero as an index value. You need to create an index variable that indexes values of x. Do this:
 N = 100;
 x = linspace(0,10,N);
 y = x.^2;
 % If you want to plot it
 plot(x,y)
 % Then integrate
 for idx = 1:N
  % Do Simpson's method using x(idx) and y(idx)
 end
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