Numerical Analysis Programs Using Fortran 90 - University of ...

Problem: Write a Fortran program to find the value of the integral
1 dt
∫
using Simpson’s 1/3 rule with n = 6
0 2
2
( t + 1) (3t
+ 4)
! program Simpson's 1/3 Rule
dimension y(20)
f(t)=1/((t**2+1)*(3*t**2+4))**.5
a=0
b=1
n=6
h=(b-a)/n
s=0
do i=1,n+1
x=a+h*(i-1)
y(i)=f(x)
enddo
do i=1,n,2
s=s+(h/3)*(y(i)+4*y(i+1)+y(i+2))
enddo
print*,'Integration by Simpsons 1/3 Rule=',s
end
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Integration by Simpson's 1/3 rule= 4.021834 E-01
36