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

Problem: Write a Fortran program to find first derivation of the function
2 3
f ( x)
= ln(5x
) + 8x
−8
at x =1. 1 using derivation of Lagrange polynomial.
! Derivation using Lagrange Formula
f(x)=log(5*x**2)+8*x**3-8
n=4
xo=1.1
h=.1
d=0
do i=1,n
s=0
do j=1,n
if (j.eq.i) goto 10
p=1
do k=1,n
if ((k.eq.j).or.(k.eq.i)) goto 20
p=p*(-h*(k-1))/(h*(i-1)-h*(k-1))
20 enddo
s=s+p/(h*(i-1)-h*(j-1))
10 enddo
d=d+s*f(xo+h*(i-1))
enddo
print*,'The First Derivation=',d
end
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The First Derivation= 30.856790
50