sum in function of function itself (recursive)
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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.
采纳的回答
Works for me:
f = @(x)x^2;
a = 0;
b = 1;
e = 1e-4;
y = adaptive_quadratur(a,b,e,f)
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
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