How do you do Simpson’s rule in Matlab?
Simpson’s rule is a method of numerical integration that provides an approximation of a definite integral over the interval [a,b] using parabolas. Generally, the function f(x) over interval [a,b] can be approximated as .
int (b,a)f (x)dx~b-a/6 [f (a)+4f (a+b/2)+f (b)]
This form works well when the function is “smooth” over [a,b]; that is, if the function doesn’t oscillate much. If the function is not smooth (which is the more common situation), the interval can be broken into subintervals, and Simpson’s rule applied. The integral of a function f(x) over the interval [a,b] with subintervals, ( a=x0 <x1 <x2… <xn=b) and subinterval length, (x=b-a/x) can be approximated as ,
int (b,a)f (x)dx~h/3 [f (x0)+4f (x1)+2f (x2)+…4f (x (x-1))+f (xn)] as long as n is even.