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

Problem: Write a Fortran program to find first derivation from the
following data at x = 0. 1 using derivation of Lagrange
polynomial.
x 0.1 0.2 0.3 0.4
y 0.01 0.04 0.09 0.16
! Derivation using Lagrange Formula
dimension x(40),y(40)
n=4
xx=0.1
data (x(i), i=1,4)/.1,.2,.3,.4/
data (y(i), i=1,4)/.01,.04,.09,.16/
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*(xx-x(k))/(x(i)-x(k))
20 enddo
s=s+p/(x(i)-x(j))
10 enddo
d=d+s*y(i)
enddo
print*,'The First Derivation=',d
end
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The First Derivation= 2.000000E-01
48