Consider
the nonlinear equation f(x)=4x2 –exp(x). Write a Fortran program
that uses the Golden Section Search Method to find the solution accurate to
within 10-6 for the nonlinear equation on [4,8].
Sauce Code:
Program Assignmentq2
implicit none
real:: f
real::x, r, q1, q2,a, b, tol=1.0e-6
!Define Interval and Function
f(x) = 4*x**2-exp(x)
a=4
b=8
print*, "a", a, "b", b
!Evaluation of the function at the end point
r=(sqrt(5.0)-1)/2
q1=b-r*(b-a)
q2=a+r*(b-a)
print*, "q1",q1, "q2", q2
! Creating Loop
!if ((b-a)<=tol) stop
do while ((b-a)>tol)
!if(f(a)*f(b)<=0) then
if(f(a)*f(q2)<=0) then
b=q2
q2=q1
q1=b-r*(b-a)
else
a=q1
q1=q2
q2=a+r*(b-a)
print*, "q1",q1, "q2", q2,
"a", a, "b", b
end if
end do
end program assignmentq2
