sum in function of function itself (recursive)

I have following Problem:

I want to calculate an adaptive Quadrature recursively. My Quadratur formula U is given by two funcitons S and T.

This is my code, where a and b are the endpoints of my interval, e is the error tolerance, and f is the function:

function y=adaptive_quadratur(a,b,e,f)

S=((b-a)/6)*(f(a)+4*f((a+b)/2)+f(b))

T=(b-a)/12*(f(a)+4*f((3*a+b)/4)+2*f((a+b)/2)+4*f((a+3*b)/4)+f(b))

U=T+(T-S)/15

if abs(T-S)<=e*(b-a)

y=U;

return

end

adaptive_quadratur(a,(a+b)/2,e,f) + adaptive_quadratur((a+b)/2,b,e,f)

end

However Matlab gives me an Error for my last line, but I dont know why.

Answer 1

[Torsten]

Works for me:

f = @(x)x^2;
a = 0;
b = 1;
e = 1e-4;
y = adaptive_quadratur(a,b,e,f)

y = 0.3333

function y=adaptive_quadratur(a,b,e,f)
  S=((b-a)/6)*(f(a)+4*f((a+b)/2)+f(b));
  T=(b-a)/12*(f(a)+4*f((3*a+b)/4)+2*f((a+b)/2)+4*f((a+3*b)/4)+f(b));
  U=T+(T-S)/15;
  if abs(T-S)<=e*(b-a)
    y=U;
    return
  end
  y = adaptive_quadratur(a,(a+b)/2,e,f) + adaptive_quadratur((a+b)/2,b,e,f)
end

[Julian]

Thank you, I also just solved my issue using ChatGPT. I was missing an "y=" in front of my last line.

So this would be my working code:

function y=adaptive_quadratur(a,b,e,f)
    S=((b-a)/6)*(f(a)+4*f((a+b)/2)+f(b));
    T=(b-a)/12*(f(a)+4*f((3*a+b)/4)+2*f((a+b)/2)+4*f((a+3*b)/4)+f(b));
    U=T+(T-S)/15
    if abs(T-S)<=e*(b-a)
        y=U;
        return
    end
    y=adaptive_quadratur(a,(a+b)/2,e,f) + adaptive_quadratur((a+b)/2,b,e,f)
end