My Profile
Active Members
TodayLast 7 Days
more...
Awards & Gifts
Online Exams
Fresher Jobs
Our fresher job section is exclusively for fresh graduates! Find jobs for freshers in major Indian
cities including Bangalore, Chennai, Hyderabad, Pune or Kochi
Resources
Find educational articles, blogs, discussion threads and other resources.
Colleges
Find details about any college in India or search for courses.
|
solving Newton Raphson Method using Fortran
Posted Date: 12 Mar 2008 Resource Type: Articles/Knowledge Sharing Category: Computer & Technology
|
Posted By: ashish singh Member Level: Diamond
Rating:  Points: 5
|
|
|
NEWTON RAPHSON METHOD
Newton Raphson Method is a very useful,simple and important method for solving all types of Transcendental and Algebric Equation. Contrary to Bisection Method and Regula Falsi, this method uses only single guess value for getting the solution of F(x)=0 provided f`(x) exists.
This method can be used to find solution for F(x)=0 only if the function f(x) is differentiable.
Let us consider x0 the initial guess and x1 is the solution of the Equation. Further x1=x0+h, where h is a constant. Using Taylor`s expression series we know that for small h F(x1)=F(x0+h)=F(x0)+hF`(x0)+(h*h)/2!*F``(x0)+…………
Neglecting high order derivatives, this can be written as
F(x1)=F(x0)+hF`(x0)
Since x1 is the solution of Equation F(x)=0,
F(x1)~0
=> F(x0)+h*F`(x0)=0 (x1-x0=h)
? F(x0)=-hF`(x0)
? H=-F(x0)/F`(x0)
X1-x0=-F(x0)/F`(x0)
=>x1=x0-F(x0)/F`(x0)
This is called Newton Raphson Formula for next guess.
Further using iterative method next guess can be estimated as
X2=x1-f(x1)/f`(x1)
…… … … …
…… … … …
xn+1=xn-F(xn)/F`(xn)
The process is terminated if |F(xn+1-xn)/xn| Where e represent apsolon which is tolerance limit.
Fortran Program for Newton Raphson Method :
C PROGRAM TO SOLVE EQUATION BY USING
C NEWTON-RAPHSON METHOD
FUNCTION F(X)
X2=X*X
F=X*X2-3*X2+2*X-1
RETURN
END
FUNCTION F1(X)
F1=3*X*X-6*X+2
RETURN
END
5 WRITE(*,*)'ENTER INITIAL GUESS'
READ(*,*) X0
WRITE(*,*)'ENTER TOLERRENCE'
READ(*,*) EPS
10 X1=X0-F(X0)/F1(X0)
IF(ABS((X1-X0)/X0).LT.EPS) THEN
WRITE(*,1) X1
1 FORMAT('SOLUTION=',F10.4)
STOP
ELSE
X0=X1
GO TO 10
ENDIF
END
Output
D:\FORTRAN\BINB>NEWTON
ENTER INITIAL GUESS
3
ENTER TOLERRENCE
.01
OLUTION= 2.3247
Stop - Program terminated.
|
Responses
|
No responses found. Be the first to respond and make money from revenue sharing program.
|
|
Watch TV Channels
|