rem system of non linear equations solver


 PRINT "PROGRAM WITH PIVOTING STRATEGY"
 A=15
 DIM C(A,A),F(A),D(A,A),G(A),X(A),S(A),E(A),A(A)
GOSUB 1020
 PRINT "NUMBER OF EQUATIONS =";NR
 M=NR:N=M+1
 PRINT" ALL GUESSES =1"

 T=.01'STEP IN NUMDER, TRY TO CHANGE IT
 PP=200'MAX ITERATIONS

 REM ***** GUESS INITIAL ROOTS ******
    FOR J=1 TO M
        PRINT "X";J;A$(J);
        INPUT "     ";AA: S(J)=AA
    NEXT J

 REM ***** CALCULATION OF COEFFICIENTS *****
 FOR Q=1 TO PP
GOSUB 2020
    FOR I=1 TO M
      F(I)=A(I)
    NEXT I
    FOR J=1 TO M
      S(J)=S(J)+T
GOSUB 2020
        FOR I=1 TO M
          D(I,J)=(A(I)-F(I))/T
        NEXT I
        S(J)=S(J)-T
    NEXT J
    FOR I=1 TO M
      G(I)=(-1)*F(I)
         FOR J=1 TO M
           G(I)=G(I)+S(J)*D(I,J)
         NEXT J
    NEXT I
    FOR I=1 TO M
      C(I,N)=G(I)
        FOR J=1 TO M
          C(I,J)=D(I,J)
          'print USING("#######.###",C(I,J));
        NEXT J
          'priNT USING("#######.###",C(I,N))
    NEXT I

 REM ******* SOLVING OF LINEARIZED EQUATION SYSTEM *****
 FOR J=1 TO M
        MYI=J
        [LOOPMYI]
        I=MYI
        C(I,J)=C(I,J)+10^(-12)'TO PLANT A SEED TO CHEAT
        IF C(I,J)<>0 GOTO [CALC]
        MYI=MYI+1
        IF MYI<=M THEN [LOOPMYI]
        PRINT "SORRY NO UNIQUE SOLUTION"
        PRINT "PRESS ENTER TO END"
        END

  [CALC]
    FOR K=1 TO N
      X=C(J,K)
      C(J,K)=C(I,K)
      C(I,K)=X
    NEXT K
    Y=1/C(J,J)
    FOR K=1 TO N
      C(J,K)=Y*C(J,K)
    NEXT K
    FOR I=1 TO M
      IF I=J goto [leap]
      Y=(-1)*C(I,J)
        FOR K=1 TO N
          C(I,K)=C(I,K)+Y*C(J,K)
        NEXT K
     [leap]
    NEXT I
 NEXT J
 PRINT
 PRINT"  *** SOLUTION VECTOR ***"
 CC=0
    FOR J=1 TO M
        X(J)=C(J,N)
        H=(X(J)-S(J))/S(J)
        CC=CC+H
        PRINT J;"   ";A$(J);"    ";INT(X(J)*1000 +.5)/1000
        S(J)=X(J)
    NEXT J
    PRINT "error  =";CC
    IF ABS(CC)<(.000001) THEN GOTO [END]
 NEXT Q

 [END]
    PRINT "PRESS ENTER TO END"
    INPUT R$
    PRINT "   **** END ****"
 END

1020 REM *** SUBROUTINE NUMBER OF EQUATIONS ***
     NR=5
     RETURN

2020 REM  **** SUBROUTINE EQUATIONS ****'TO USE: CHANGE AT 2 LOCATIONS IN THE MAIN PROGRAM
     S1=S(1): S2=S(2): S3=S(3): S4=S(4): S5=S(5)
     S6=S(6): S7=S(7): S8=S(8): S9=S(9): S10=S(10)
     REM ******************************
     A(1)=S1+S2-3
     A(2)=S1+S2^(2)-5
     A(3)=S1^(2)+S4^(2)-17
     A(4)=S5+S3^(2)-14
     A(5)=S4+S5-9

     A$(1)=" ROOT1 ":A$(2)=" ROOT2 ":A$(3)=" ROOT3 "
     A$(4)=" ROOT4 ":A$(5)=" ROOT5 ":A$(6)="   "
     A$(7)="  ":A$(8)=" ":A$(9)="    "
     RETURN


1060 REM *** SUBROUTINE NUMBER OF EQUATIONS ***
     NR=9
     RETURN

2060 REM  **** SUBROUTINE EQUATIONS ****
     S1=S(1): S2=S(2): S3=S(3): S4=S(4): S5=S(5)
     S6=S(6): S7=S(7): S8=S(8): S9=S(9): S10=S(10)
     REM ******************************
'          SUB 6
     PT=1    'pressure
     T1=1000   'temp K
      MO2=2'MOL
      MH2=.5'MOL
      MC =1'MOL
      MN2=6'MOL
      'K1=2.155*10^(6)*EXP(-13667/T1)   'C+H20
      K2=.00574*EXP(5691/T1)            'SHIFT
      K3=5.22*10^(-11)*EXP(9367/T1)     'NH3
      K4=3.5*10^(-5)*EXP(8224/T1)       'CH4 1100K
      K5=9.6610^(-10)*EXP(67835/T1)     '2C0+O2

     A(1)=K5*S2^(2)*S1           -S3^(2)       'C0 +1/2O2
     A(2)=K2*S2*S5               -S3*S4        'SHIFT EQ
     A(3)=K3*S7*S4^(3)           -S8^(2)       'NH3 EQ
     A(4)=K4*S4^(2)              -S9+10^(-10)  'CH4 EQ
     A(5)=S2+S3+S9               -PT/S6*MC     'C BAL.
     A(6)=S4+S5+2*S9+1.5*S8      -PT/S6*MH2    'H2 BAL
     A(7)=S2+2*S3+S5+2*S1        -PT/S6*MO2*2  'O BAL
     A(8)=S8+2*S7                -PT/S6*MN2*2  'N BAL.
     A(9)=S1+S2+S3+S4+S5+S7+S8+S9-PT           'DALTON

     A$(1)=" O2    ":A$(2)=" C0    ":A$(3)=" CO2   "
     A$(4)=" H2    ":A$(5)=" H20   ":A$(6)=" NTOT  "
     A$(7)=" N2    ":A$(8)=" NH3   ":A$(9)=" CH4   "

'    1=O2  2=CO 3=C02 4=H2  5=H20  6=NTOT  7=N2   8=NH3  9=CH4
   ' A$(1)="CH4;   2";A$(2)="CO    "
     RETURN