Hi
this is pdf : http://www.cs.umd.edu/~elman/460.10/final/final.pdf
I have question with problem 1
I solved problem 1 but i am not sure if my answers are right.:(
can you check?? plz!!
my answers
for a) i said,
if applying the composite simpson rule on a uniform mesh subdividing [a,b] into intervals of width h/2, two halves of the interval are [a,c] [c,b]
and d,e are midpoints of these two subintervals
d= (a+c)/2 , e= (c+b)/2
apply Simpson's rule to each subinterval, a quadrature rule on [a,b]
S_2 = h/12 ( f(a)+4f(B)+2f(c)+4f(e)+f(b) )
so, S_2 = I(f)- (1/15) (S_2(f)-S(f))
for a) i said,
The two can be combined to get an even more accurate approximation Q
Both rules are of order 4, but step size for S_2 is half the size for S, so the error in S_2 is roughly 2^4=16 times smaller than that of S.
Thus, a new, more accurate rule Q can be obtained by solving
Q-S=16(Q-S_2)
so, S(f)=S_2(f)+ 1/15 ((S_(f)-S(f))
to compute integral[0, pi/2] cos(x) dx,
code:
f=inline('cos(x)')
Q=quad(f,0,pi/2)
and i have no idea what to do with part (c)
can anyone help me?!!!! plz!!!!