Adam Moulton method

https://souravrohan.wordpress.com/2011/06/05/adam-moulton-method/

Adam Moulton method

FORTRAN CODE FOR SOLVING An IVP USING Adam Moulton  4-STEP IMPLICIT METHOD:

PARAMETER(M=10)
OPEN(33,FILE=’INP14.DAT’)
OPEN(34,FILE=’OUP14.DAT’)
READ(33,*)A,B,H,W0
CALL AM(A,B,H,W0,M)
END PROGRAM

SUBROUTINE AM(A,B,H,W0,M)
REAL K1,K2,K3,K4,W(M),T(M),N
WRITE(34,10)
10 FORMAT(2X,’X’,9X,’EXACT’,12X,’AMW(I)’,10X,’ERR’)
N=(B-A)/H
W(0)=W0
T(0)=A
WRITE(34,11)T(0),G(T(0)),W(0), ABS(G(T(0))-W(0))
11 FORMAT(2X,F4.2,3(4X,F12.8))

DO I=1,4
K1=H*F(T(I-1),W(I-1))
K2=H*F(T(I-1)+H/2,W(I-1)+K1/2)
K3=H*F(T(I-1)+H/2,W(I-1)+K2/2)
K4=H*F(T(I-1)+H,W(I-1)+K3)
W(I)=W(I-1)+(K1+2*K2+2*K3+K4)/6.0
T(I)=A+I*H
WRITE(34,11)T(I),G(T(I)),W(I), ABS(G(T(I))-W(I))
END DO
DO I=3,N-1
T(I+1)=A+(I+1)*H
W(I+1)=W(I)+(H/720)*(251*F(T(I+1),W(I+1))+646*F(T(I),W(I))-264*F(T(I-1),W(I-1))+106*F(T(I-2),W(I-2))-19*F(T(I-3),W(I-3)))
WRITE(34,11)T(I+1),G(T(I+1)),W(I+1), ABS(G(T(I+1))-W(I+1))
END DO
END SUBROUTINE

FUNCTION F(T,Y)
F=COS(2*T)+SIN(3*T)
RETURN
END

FUNCTION G(T)
G=SIN(2*T)/2.0-(COS(3*T)-4)/3.0
RETURN
END

inputs:
0
2
0.2
0.5

program name:

outputs:
X EXACT AMW(I) ERR
0.00 1.00000000 1.00000000 0.00000003
0.20 1.25293064 1.15557957 0.09735110
0.40 1.57122552 1.39189768 0.17932783
0.60 1.87508702 1.64209783 0.23298915
0.80 2.07891798 1.82905316 0.24986494
0.80 2.07891798 1.82908905 0.24982905
1.00 2.11797953 1.89059699 0.22738262

SEE NUMERICAL ANALYSIS (7TH EDITION) BY BURDEN
PAGE 295 TO KNOW MORE………………………………