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

Problem: Write a program to determine the roots of the equation
4
3
2
x −1.99x
−1.76x
+ 5.22x
− 2.23 = 0 that are close to x = 1. 5
by Newton-Raphson method.
f(x)=x**4-1.99*x**3-1.76*x**2+5.22*x-2.23
df(x)=4*x**3-5.97*x**2-3.52*x+5.22
ddf(x)=12*x**2-11.94*x-3.52
tol=0.00001
xo=1.5
10 x=xo-df(xo)/ddf(xo)
if(abs(x-xo).lt.tol) goto 20
xo=x
goto 10
20 eps=sqrt(-2*f(x)/ddf(x))
y1=x+eps
30 y=y1-f(y1)/df(y1)
if(abs(y-y1).lt.tol) goto 40
print *,y
y1=y
goto 30
40 print *,'The First Root is',y
print*,'************************'
y1=x-eps
50 y=y1-f(y1)/df(y1)
if(abs(y-y1).lt.tol) goto 60
print *,y
y1=y
goto 50
60 print *,'The Second Root is',y
end
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
1.565973
1.565888
The First Root is 1.565888
************************************
1.424016
1.424112
The Second Root is 1.424112
++++++++++++++++++++++++++
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