!!!!!!!!!!!!!!!!!!!!!!!!!!! Program 2.8 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! !
! Please Note: !
! !
! (1) This computer program is written by Tao Pang in conjunction with !
! his book, "An Introduction to Computational Physics," published !
! by Cambridge University Press in 1997. !
! !
! (2) No warranties, express or implied, are made for this program. !
! !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
PROGRAM ROOT
!
! Main program to use the Secant Method to find the root of
! f(x)=exp(x)*ln(x)-x*x=0. Copyright (c) Tao Pang 1997.
!
IMPLICIT NONE
INTEGER :: ISTEP
REAL :: A,B,DL,DX,X0
!
DL = 1.0E-06
A = 1.0
B = 2.0
DX = (B-A)/10.0
X0 = (A+B)/2.0
CALL SECANT (DL,X0,DX,ISTEP)
WRITE (6,"(I4,2F16.8)") ISTEP,X0,DX
END PROGRAM ROOT
!
SUBROUTINE SECANT (DL,X0,DX,ISTEP)
!
! Subroutine for the root of f(x)=0 with the secant method.
! Copyright (c) Tao Pang 1997.
!
IMPLICIT NONE
INTEGER, INTENT (INOUT) :: ISTEP
REAL, INTENT (INOUT) :: X0,DX
REAL :: X1,X2,D,F,FX
REAL, INTENT (IN) :: DL
!
ISTEP = 0
X1 = X0+DX
DO WHILE (ABS(DX).GT.DL)
D = FX(X1)-FX(X0)
X2 = X1-FX(X1)*(X1-X0)/D
X0 = X1
X1 = X2
DX = X1-X0
ISTEP = ISTEP+1
END DO
END SUBROUTINE SECANT
!
FUNCTION FX(X) RESULT (F)
IMPLICIT NONE
REAL :: F
REAL, INTENT (IN) :: X
!
F = EXP(X)*ALOG(X)-X*X
END FUNCTION FX