A_02 JACOBIAN NEWTON'S ITERATIVE METHOD, Fortran

A_02 JACOBIAN NEWTON'S ITERATIVE METHOD

PROGRAM N_I_M
IMPLICIT NONE
REAL::X,Y,F1,F2,DXF1,DYF1,DXF2,DYF2,MAT(3,2),TOL,PI=3.1415926,e=2.718281
INTEGER::I,J,K,N
PRINT*,'INPUT THE VALUE OF TOL:'
READ*,TOL
PRINT*,'INPUT THE VALUE OF N:'
READ*,N
X=2.0
Y=2.0
DO I=1,N
    MAT(1,1)=DXF1(X,Y)
    MAT(2,1)=DYF1(X,Y)
    MAT(3,1)=-1.0*F1(X,Y)
    MAT(1,2)=DXF2(X,Y)
    MAT(2,2)=DYF2(X,Y)
    MAT(3,2)=-1.0*F2(X,Y)
CALL NEW(MAT)
X=X+MAT(3,1)
Y=Y+MAT(3,2)
WRITE (*,20)X,Y
20 FORMAT (' THE ROOT IS:',F6.3)

IF((ABS(MAT(3,1))<=TOL).OR.(ABS(MAT(3,2))<=TOL)) EXIT
END DO
PRINT*,'THE JACOBIAN MATRIX IS:'
PRINT*,MAT
STOP
END PROGRAM N_I_M

REAL FUNCTION F1(X,Y)
IMPLICIT NONE 
REAL::X,Y,PI
F1=LOG(ABS(X-Y**2.0))-SIN(X*Y)-SIN(PI)
RETURN
END FUNCTION F1

REAL FUNCTION DXF1(X,Y)
IMPLICIT NONE 
REAL::X,Y
DXF1=(1/(X-Y**2.0))-Y*COS(X*Y)
RETURN
END FUNCTION DXF1

REAL FUNCTION DYF1(X,Y)
IMPLICIT NONE 
REAL::X,Y
DYF1=((1/(X-Y**2.0))*(-2.0*Y))-X*COS(X*Y)
RETURN 
END FUNCTION DYF1

REAL FUNCTION F2(X,Y)
IMPLICIT NONE
REAL::X,Y,e
F2=e**(X*Y)+COS(X-Y)+2.0
RETURN 
END FUNCTION F2
 
REAL FUNCTION DXF2(X,Y)
IMPLICIT NONE
REAL::X,Y,e
DXF2=Y*e**(X*Y)-SIN(X-Y)
RETURN 
END FUNCTION DXF2

REAL FUNCTION DYF2(X,Y)
IMPLICIT NONE
REAL::X,Y,e
DYF2=X*e**(X*Y)+SIN(X-Y)
RETURN 
END FUNCTION DYF2

SUBROUTINE NEW(MAT)
REAL::MAT(3,2),D
INTEGER::I,J,K
DO K=1,2
   D=MAT(K,K)
   DO I=1,3
     MAT(I,K)=MAT(I,K)/D
   END DO
    
     DO J=1,2
       IF(K==J) CYCLE
        D= MAT(K,J)
           DO I=1,3
              MAT(I,J)=MAT(I,J)-(MAT(I,K)*D)
           END DO
     END DO
END DO
RETURN
END SUBROUTINE NEW


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