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Fig 4.11
========



00001 IMPLICIT REAL*8 (A-H,O-Z)
00002 IMPLICIT INTEGER*4(I-N)
00003 DIMENSION U0(41),Z(41),U(41,260),Z0(41)
00004 EXTERNAL AK
00005 X1=0.
00006 X2=1.
00007 Y1=-2.
00008 Y2=2.
00009 N=41
00010 M=41
00011 IMAX=400
00012 IC=3
00013 DL=0.
00014 DO 1 J=1,N
00015 X=X1+(X2-X1)/(N-1.)*(J-1.)
00016 1 Z0(J)=4.*X*(1.-X)
00017 CALL PTICR0(AK,U,X1,X2,Y1,Y2,N,M)
00018 CALL PTICR3(U,Z0,U0,N,M)
00019 DO 4 J=1,N
00020 Z(J)=0.
00021 4 CONTINUE
00022 CALL PTISR(AK,U0,X1,X2,Y1,Y2,N,M,Z,AN,
*ITER,DL,IMAX,IC,U,41*260,IERR)
00023 PRINT 5,Z0,Z,DL,AN,ITER,IERR
00024 STOP
00025 5 FORMAT(15X,'Exact Solution:'/'.'/
* 8(5F11.6/),F11.6/'.'/
*15X,'Approximate solution:'/'.'/
* 8(5F11.6/),F11.6/'.'/
*10X,'Right side error square :',
* D14.6/
*10X,'Discrepancy :',
* D14.6/
*10X,'Number of iterations :',
* I14/
*10X,'Return code (IERR) :',
* I14)
00026 END


00001 FUNCTION AK(X,Y)
00002 IMPLICIT REAL*8(A-H,O-Z)
00003 AK=1./(1.+100.*(X-Y)**2)
00004 RETURN
00005 END






Exact solution:

.000000 .097500 .190000 .277500 .360000
.437500 .510000 .577500 .640000 .697500
.750000 .797500 .840000 .877500 .910000
.937500 .960000 .977500 .990000 .997500
1.000000 .997500 .990000 .977500 .960000
.937500 .910000 .877500 .840000 .797500
.750000 .697500 .640000 .577500 .510000
.437500 .360000 .277500 .190000 .097500
.000000

Approximate solution:

.000000 .097502 .189998 .277498 .360000
.437501 .510001 .577501 .639999 .697499
.749999 .797500 .840000 .877500 .910000
.937500 .960000 .977500 .990000 .997500
1.000000 .997500 .990000 .977500 .960000
.937500 .910000 .877500 .840000 .797500
.749999 .697499 .639999 .577501 .510001
.437501 .360000 .277498 .189998 .097502
.000000

Right side error square : .000000D+00
Discrepancy : .946349D-18
Number of iterations : 90
Return code (IERR) : 0
Fig 4.2
=======


00001 IMPLICIT REAL*8(A-H,O-Z)
00002 IMPLICIT INTEGER*4(I-N)
00003 DIMENSION Z0(41),U0(41),U(5000),Z(41)
00004 EXTERNAL AK
00005 X1=0.
00006 X2=1.
00007 Y1=-2.
00008 Y2=2.
00009 N=41
00010 M=41
00011 IMAX=1000
00012 C1=1.001
00013 ALFA=0.0004
00014 HX=(X2-X1)/(N-1.)
00015 CALL PTICR0(AK,U,X1,X2,Y1,Y2,N,M)
00016 H=1.E-10
00017 DO 57 I=1,N
00018 X=X1+HX*(I-1.)
00019 Z0(I)=(DEXP(-(X-0.3)**2/0.03)+
+DEXP(-(X-0.7)**2/0.03))/0.955040800-
-0.0521309113
00020 57 CONTINUE
00021 CALL PTICR3(U,Z0,U0,N,M)
00022 PRINT 501,(Z0(II),II=1,N)
00023 501 FORMAT(1X,'Exact solution='/(5F11.7))
00024 DL=1.E-8
00025 PRINT 502,H,DL
00026 502 FORMAT(' .'/
*' Errors: in operator -',D16.9/
*' in right side -',D16.9)
00027 CALL PTIMR(AK,U0,X1,X2,Y1,Y2,N,M,Z,AN2,
*DL,H,C1,IMAX,ALFA,U,10000,IERR)
00028 PRINT 503,(Z(II),II=1,N)
00029 PRINT 504,IERR,AN2,ALFA
00030 503 FORMAT(' .'/
* ' Approximate solution:'/(5F11.7))
00031 504 FORMAT(' .'/
* ' Return code :',I5/
* ' Discrepancy :',D16.9/
* ' Regularization parameter :',D16.9)
00032 STOP
00033 END


00001 FUNCTION AK(X,Y)
00002 IMPLICIT REAL*8(A-H,O-Z)
00003 AK=1./(1.+100.*(X-Y)**2)
00004 RETURN
00005 END




Exact solution=
.0000000 .0320465 .0782459 .1415609 .2238816
.3251418 .4425163 .5699656 .6983832 .8164924
.9124512 .9758983 1.0000000 .9829996 .9288697
.8468924 .7502625 .6540357 .5728488 .5188144
.4998815 .5188144 .5728488 .6540357 .7502625
.8468924 .9288697 .9829996 1.0000000 .9758983
.9124512 .8164924 .6983832 .5699656 .4425163
.3251418 .2238816 .1415609 .0782459 .0320465
.0000000
.
Errors: in operator - .100000001D-09
in right side - .999999994D-08
.
Approximate solution:
.0173081 .0311578 .0715787 .1366338 .2238399
.3296361 .4487824 .5745464 .6991498 .8137768
.9084307 .9725681 .9974897 .9802096 .9256576
.8447169 .7506126 .6567675 .5762364 .5213060
.5017045 .5213060 .5762364 .6567675 .7506126
.8447169 .9256576 .9802096 .9974897 .9725681
.9084308 .8137768 .6991498 .5745464 .4487824
.3296361 .2238399 .1366338 .0715788 .0311579
.0173083
.
Return code : 0
Discrepancy : .178224579D-07
Regularization parameter : .244141280D-06

Fig 4.3
=======



00001 IMPLICIT REAL*8(A-H,O-Z)
00002 IMPLICIT INTEGER*4(I-N)
00003 DIMENSION U0(41),Z(41),U(5000),Z0(41)
00004 EXTERNAL AK
00005 X1=0.
00006 X2=1.
00007 Y1=-2.
00008 Y2=2.
00009 N=41
00010 M=41
00011 IMAX=1000
00012 C1=1.001
00013 ALFA=0.000001
00014 HX=(X2-X1)/(N-1.)
00015 CALL PTICR0(AK,U,X1,X2,Y1,Y2,N,M)
00016 H=1.E-10
00017 DO 57 I=1,N
00018 X=X1+HX*(I-1.)
00019 Z0(I)=(DEXP(-(X-0.5)**2/0.06))
00020 57 CONTINUE
00021 PRINT 501,(Z0(II),II=1,N)
00022 501 FORMAT(1X,'Exact solution='/(5F11.7))
00023 CALL PTICR3(U,Z0,U0,N,M)
00024 DL=1.E-8
00025 PRINT 502,H,DL
00026 502 FORMAT(' .'/
*' Errors: in operator -',D16.9/
*' in right side -',D16.9)
00027 DO 34 I=1,N
00028 34 Z(I)=0.
00029 CALL PTIZR(AK,U0,X1,X2,Y1,Y2,N,M,Z,
*IC,AN2,DL,H,C1,ANGRD,IMAX,ALFA,U,
*10000,IERR)
00030 PRINT 503,(Z(II),II=1,N)
00031 PRINT 504,IERR,AN2,ALFA
00032 503 FORMAT(' .'/
*' Approximate solution:'/(5F11.7))
00033 504 FORMAT(' .'/
*' Return code :',I5/
*' Discrepancy :',D16.9/
*' Regularization parameter :',D16.9)
00034 STOP
00035 END


00001 FUNCTION AK(X,Y)
00002 IMPLICIT REAL*8(A-H,O-Z)
00003 AK=1./(1.+100.*(X-Y)**2)
00004 RETURN
00005 END





Exact solution=
.0155039 .0232740 .0342181 .0492711 .0694834
.0959671 .1298122 .1719732 .2231302 .2835359
.3528661 .4300946 .5134171 .6002454 .6872893
.7707304 .8464817 .9105104 .9591895 .9896374
1.0000000 .9896374 .9591895 .9105104 .8464817
.7707304 .6872893 .6002454 .5134171 .4300946
.3528661 .2835359 .2231302 .1719732 .1298122
.0959671 .0694834 .0492711 .0342181 .0232740
.0155039
.
Errors: in operator - .100000001D-09
in right side - .999999994D-08
.
Approximate solution:
.0211643 .0240784 .0328794 .0475972 .0684072
.0957261 .1302309 .1728098 .2243091 .2850577
.3545593 .4316402 .5146232 .6011371 .6878841
.7708297 .8457517 .9088284 .9568809 .9871938
.9975960 .9871938 .9568809 .9088284 .8457517
.7708297 .6878841 .6011371 .5146232 .4316402
.3545593 .2850577 .2243092 .1728098 .1302309
.0957261 .0684072 .0475972 .0328794 .0240785
.0211644
.
Return code : 0
Discrepancy : .151755068D-07
Regularization parameter : .929922913D-06

Fig 4.4
=======



00001 IMPLICIT REAL*8(A-H,O-Z)
00002 IMPLICIT INTEGER*4(I-N)
00003 DIMENSION U0(41),Z(41),U(10000),Z0(41)
00004 EXTERNAL AK
00005 X1=0.
00006 X2=1.
00007 Y1=-2.
00008 Y2=2.
00009 N=41
00010 M=41
00011 IMAX=1000
00012 C1=1.001
00013 IC=0
00014 ALFA=0.000001
00015 HX=(X2-X1)/(N-1.)
00016 CALL PTICR0(AK,U,X1,X2,Y1,Y2,N,M)
00017 H=1.E-10
00018 DO 57 I=1,N
00019 X=X1+HX*(I-1.)
00020 Z0(I)=(DEXP(-(X-0.5)**2/0.06))
00021 57 CONTINUE
00022 PRINT 501,(Z0(II),II=1,N)
00023 501 FORMAT(1X,'Exact solution='/(5F11.7))
00024 CALL PTICR3(U,Z0,U0,N,M)
00025 DL=1.D-8
00026 PRINT 502,H,DL
00027 502 FORMAT(' .'/
*' Errors: in operator -',D16.9/
*' in right side -',D16.9)
00028 DO 34 I=1,N
00029 34 Z(I)=0.5
00030 CALL PTIPR(AK,U0,X1,X2,Y1,Y2,N,M,Z,IC,
*AN2,DL,H,C1,ANGRD,IMAX,ALFA,U,
*10000,IERR)
00031 PRINT 503,(Z(II),II=1,N)
00032 PRINT 504,IERR,AN2,ALFA
00033 503 FORMAT(' .'/
*' Approximate solution:'/(5F11.7))
00034 504 FORMAT(' .'/
*' Return code :',I5/
*' Discrepance :',D16.9/
*' Regularization parameter :',D16.9)
00035 STOP
00036 END


00001 FUNCTION AK(X,Y)
00002 IMPLICIT REAL*8(A-H,O-Z)
00003 AK=1./(1.+100.*(X-Y)**2)
00004 RETURN
00005 END






Exact solution=
.0155039 .0232740 .0342181 .0492711 .0694834
.0959671 .1298122 .1719732 .2231302 .2835359
.3528661 .4300946 .5134171 .6002454 .6872893
.7707304 .8464817 .9105104 .9591895 .9896374
1.0000000 .9896374 .9591895 .9105104 .8464817
.7707304 .6872893 .6002454 .5134171 .4300946
.3528661 .2835359 .2231302 .1719732 .1298122
.0959671 .0694834 .0492711 .0342181 .0232740
.0155039
.
Errors: in operator - .100000001D-09
in right side - .100000000D-07
.
Approximate solution:
.0210491 .0239928 .0328555 .0476350 .0684788
.0957898 .1302494 .1727642 .2242018 .2849067
.3543894 .4314756 .5144849 .6010413 .6878428
.7708505 .8458373 .9089764 .9570818 .9874308
.9978459 .9874308 .9570818 .9089764 .8458374
.7708505 .6878428 .6010413 .5144849 .4314756
.3543894 .2849068 .2242018 .1727642 .1302494
.0957897 .0684788 .0476350 .0328555 .0239929
.0210492
.
Return code : 67
Discrepancy : .124056379D-07
Regularization parameter : .838278424D-06

Fig 4.5
=======


00001 IMPLICIT REAL*8(A-H,O-Z)
00002 IMPLICIT INTEGER*4(I-N)
00003 REAL*8 KERN,L1,L2
00004 DIMENSION U(400),U0(64),Z0(64),Z(64),
*KERN(64)
00005 EXTERNAL AK
00006 C=0.0
00007 D=2.0
00008 L1=0.0
00009 L2=1.0
00010 ALPHA=1.0
00011 C1=1.000001
00012 N=64
00013 IMAX=500
00014 ST=(D-C)/N
00015 DO 5 I=1,N
00016 S=(I-0.5)*ST-0.5
00017 Z0(I)=0.
00018 IF(S.LT.0.0.OR.S.GT.1.0)GOTO 5
00019 Z0(I)=((DEXP(-(S-0.3)**2/0.03)+
+DEXP(-(S-0.7)**2/0.03))/0.955040800-
-0.052130913)*1.4*S
00020 5 CONTINUE
00021 DO 554 K=1,N
00022 S=0.5*(L1+L2)+ST*(K-N/2-1)
00023 KERN(K)=0.
00024 IF(S.LT.L1.OR.S.GT.L2)GOTO 554
00025 KERN(K)=AK(S)
00026 554 CONTINUE
00027 HH=1.E-9
00028 DO 771 I=1,N
00029 S=0.0
00030 DO 770 J=1,N
00031 IND=I-J+N/2+1
00032 IF(IND.LT.1.OR.IND.GT.N)GOTO 770
00033 S=S+KERN(IND)*Z0(J)
00034 770 CONTINUE
00035 U0(I)=S*ST
00036 771 CONTINUE
00037 DL=1.E-8
00038 PRINT 999,(Z0(I),I=1,N)
00039 999 FORMAT(' Exact solution:'/(5F11.8))
00040 PRINT 553,DL,HH
00041 553 FORMAT(' Errors:'/
*' in right side:',D16.9/
*' in operator :',D16.9)
00042 CALL PTIKR(AK,U0,A,B,C,D,L1,L2,N,Z,AN,
*DL,HH,C1,IMAX,ALPHA,U,400,IERR)
00043 PRINT 501,IERR,AN,ALPHA,
*A,B,(Z(II),II=1,N)
00044 501 FORMAT(' .'/
*' Return code (IERR) :',
* I5/
*' Discrepancy :',
* D16.9/
*' Regularization parameter :',
* D16.9/
*' Solution found on interval : (',
* F4.1,',',F3.1,')'/
*' .'/' Approximate solution:'/
* (5F11.8))
00045 STOP
00046 END


00001 FUNCTION AK(Y)
00002 IMPLICIT REAL*8(A-H,O-Z)
00003 AK=DEXP(-80.*(Y-.5)**2)
00004 RETURN
00005 END





Exact solution:
.00000000 .00000000 .00000000 .00000000 .00000000
.00000000 .00000000 .00000000 .00000000 .00000000
.00000000 .00000000 .00000000 .00000000 .00000000
.00000000 .00040570 .00469802 .01649271 .03976953
.07814444 .13325059 .20303119 .28077126 .35567888
.41531472 .44932413 .45318938 .43054079 .39307592
.35804191 .34403504 .36623085 .43211954 .53865959
.67164363 .80785932 .92004465 .98364014 .98334749
.91718612 .79650698 .64202556 .47754936 .32383759
.19461398 .09552648 .02555887 .00000000 .00000000
.00000000 .00000000 .00000000 .00000000 .00000000
.00000000 .00000000 .00000000 .00000000 .00000000
.00000000 .00000000 .00000000 .00000000
Errors:
in right side: .999999994D-08
in operator : .999999972D-09
.
Return code (IERR) : 0
Discrepancy : .344029501D-07
Regularization parameter : .573252726D-06
Solution found on interval : ( -.5,1.5)
.
Approximate solution:
-.00017321 -.00009008 .00000358 .00006029 .00008013
.00007742 .00004968 -.00001771 -.00011536 -.00018162
-.00012615 .00008648 .00034550 .00039636 .00003549
-.00048053 .00007864 .00429205 .01602516 .03971215
.07899454 .13503747 .20511177 .28210682 .35544513
.41342703 .44649610 .45048758 .42878790 .39255440
.35866264 .34570400 .36896886 .43575007 .54236307
.67392962 .80724469 .91610707 .97765767 .97787558
.91464292 .79762609 .64528134 .48012463 .32370988
.19255030 .09573080 .03446567 .00344908 -.00649811
-.00528917 -.00088940 .00212787 .00252328 .00120195
-.00032238 -.00105252 -.00086547 -.00023138 .00029757
.00044660 .00027443 .00000811 -.00015972

Fig 4.6
=======



00001 IMPLICIT REAL*8(A-H,O-Z)
00002 IMPLICIT INTEGER*4(I-N)
00003 REAL*8 KERN
00004 DIMENSION U(6500),U0(32,32),Z0(32,32),
*Z(32,32),ALIM(12),KERN(32,32)
00005 EXTERNAL AK
00006 ALIM(5)=0.
00007 ALIM(6)=2.0
00008 ALIM(7)=0.
00009 ALIM(8)=2.0
00010 ALIM(9)=0.
00011 ALIM(10)=1.0
00012 ALIM(11)=0.0
00013 ALIM(12)=1.0
00014 ALPHA=1.000
00015 C1=1.000001D0
00016 N1=32
00017 N2=32
00018 IMAX=500
00019 R=0.
00020 ST1=(ALIM(6)-ALIM(5))/N1
00021 ST2=(ALIM(8)-ALIM(7))/N2
00022 DO 5 I=1,N1
00023 DO 5 J=1,N2
00024 S1=(I-0.5)*ST1-0.5
00025 S2=(J-0.5)*ST2-0.5
00026 Z0(I,J)=0.
00027 IF(S1.LT.0.0.OR.S1.GT.1.0.OR.S2.LT.0.0.OR.S2.GT.1.0)
* GOTO 5
00028 Z0(I,J)=((DEXP(-(S1-0.3)**2/0.03)+
+DEXP(-(S1-0.7)**2/0.03))/0.9550408-
-0.052130913)*DEXP(-(S2-0.5)**2/0.03)
00029 5 CONTINUE
00030 DO 554 K=1,N1
00031 DO 554 L=1,N2
00032 S1=(ALIM(9)+ALIM(10))/2.+ST1*(K-N1/2-1)
00033 S2=(ALIM(11)+ALIM(12))/2.+ST2*(L-N2/2-1)
00034 KERN(K,L)=0.
00035 IF(S1.LT.ALIM(9).OR.S1.GT.ALIM(10).
* OR.S2.LT.ALIM(11).OR.S2.GT.ALIM(12))
* GOTO 554
00036 KERN(K,L)=AK(S1,S2)
00037 554 CONTINUE
00038 HH=3.68D-11
00039 DO 771 I1=1,N1
00040 DO 771 I2=1,N2
00041 S=0.
00042 DO 770 J1=1,N1
00043 DO 770 J2=1,N2
00044 IND1=I1-J1+N1/2+1
00045 IND2=I2-J2+N2/2+1
00046 IF(IND1.LT.1.OR.IND1.GT.N1) GOTO 770
00047 IF(IND2.LT.1.OR.IND2.GT.N2) GOTO 770
00048 S=S+KERN(IND1,IND2)*Z0(J1,J2)
00049 770 CONTINUE
00050 U0(I1,I2)=S*ST1*ST2
00051 IF(R.LT.U0(I1,I2)) R=U0(I1,I2)
00052 771 CONTINUE
00053 DL=6.32D-07
00054 PRINT 553,DL,HH
00055 553 FORMAT(' Errors :'/
*' in right side: ',D16.9/
*' in operator: ',D16.9)
00056 CALL PTITR(AK,U0,ALIM,N1,N2,Z,DL,HH,
*C1,ALPHA,AN,U,6500,IMAX,IERR)
00057 PRINT 501,IERR,AN,ALPHA
00058 501 FORMAT(' .',/
*' Return code :',I5/
*' Discrepancy :',D16.9/
*' Regularization parameter :',D16.9)
00059 PRINT 503
00060 PRINT 502,(Z0(13,I),I=1,N2),
*(Z(13,I),I=1,N2)
00061 PRINT 505
00062 PRINT 502,(Z0(I,16),I=1,N1),
*(Z(I,16),I=1,N1)
00063 502 FORMAT(' Exact solution:'/8(4F8.4/))
00064 503 FORMAT('.'/' section X=0.28125 ')
00065 505 FORMAT('.'/' section Y=0.46875 ')
00066 1000 STOP
00067 END


00001 FUNCTION AK(X,Y)
00002 IMPLICIT REAL*8(A-H,O-Z)
00003 AK=DEXP(-20.*(X-0.5)**2-20.*(Y-0.5)**2)
00004 RETURN
00005 END







Errors :
in right side: .632000000D-06
in operator: .368000000D-10
.
Return code : 0
Discrepancy : .782989588D-06
Regularization parameter : .110838081D-07

section X=0.28125
Exact solution:
.0000 .0000 .0000 .0000
.0000 .0000 .0000 .0000
.0006 .0040 .0192 .0706
.2000 .4369 .7354 .9542
.9542 .7354 .4369 .2000
.0706 .0192 .0040 .0006
.0000 .0000 .0000 .0000
.0000 .0000 .0000 .0000

-.0019 -.0033 -.0036 -.0004
.0063 .0120 .0105 -.0009
-.0155 -.0162 .0194 .1083
.2493 .4178 .5706 .6616
.6616 .5706 .4178 .2493
.1083 .0194 -.0162 -.0155
-.0009 .0105 .0120 .0063
-.0004 -.0036 -.0033 -.0019


section Y=0.46875
Exact solution:
.0000 .0000 .0000 .0000
.0000 .0000 .0000 .0000
.0408 .1950 .4586 .7633
.9542 .9152 .7023 .5123
.5123 .7023 .9152 .9542
.7633 .4586 .1950 .0408
.0000 .0000 .0000 .0000
.0000 .0000 .0000 .0000

.0044 .0074 .0075 -.0018
-.0200 -.0353 -.0265 .0277
.1366 .2878 .4498 .5836
.6616 .6810 .6637 .6431
.6431 .6637 .6810 .6616
.5836 .4498 .2878 .1366
.0277 -.0265 -.0353 -.0200
-.0018 .0075 .0074 .0044

Fig 4.7
=======

00001 IMPLICIT REAL*8(A-H,O-Z)
00002 IMPLICIT INTEGER*4(I-N)
00003 DIMENSION U0(41),Z(41),U(41,260),Z0(41)
00004 EXTERNAL AK
00005 X1=0.
00006 X2=1.
00007 Y1=-2.
00008 Y2=2.
00009 N=41
00010 M=41
00011 IMAX=400
00012 IC=2
00013 DL=0.
00014 C1=0.
00015 C2=1.
00016 DO 1 J=1,N
00017 X=X1+(X2-X1)/(N-1.)*(J-1.)
00018 1 Z0(J)=1.-X*X
00019 CALL PTICR0(AK,U,X1,X2,Y1,Y2,N,M)
00020 CALL PTICR3(U,Z0,U0,N,M)
00021 DO 4 J=1,N
00022 Z(J)=0.
00023 4 CONTINUE
00024 CALL PTIGR(AK,U0,X1,X2,Y1,Y2,N,M,Z,AN,
*ITER,DL,IMAX,C1,C2,IC,U,41*260,IERR)
00025 PRINT 5,Z0,Z,DL,AN,ITER,IERR
00026 STOP
00027 5 FORMAT(15X,'Exact solution:'/'.'/
* 8(5F11.6/),F11.6/'.'/
*15X,'Approximate solution:'/'.'/
* 8(5F11.6/),F11.6/'.'/
*10X,'Right side error square :',
* D14.6/
*10X,'Discrepancy :',
* D14.6/
*10X,'Number of iterations :',
* I14/
*10X,'Return code (IERR) :',
* I14)
00028 END


00001 FUNCTION AK(X,Y)
00002 IMPLICIT REAL*8(A-H,O-Z)
00003 AK=1./(1.+100.*(X-Y)**2)
00004 RETURN
00005 END





Exact solution:

1.000000 .999375 .997500 .994375 .990000
.984375 .977500 .969375 .960000 .949375
.937500 .924375 .910000 .894375 .877500
.859375 .840000 .819375 .797500 .774375
.750000 .724375 .697500 .669375 .640000
.609375 .577500 .544375 .510000 .474375
.437500 .399375 .360000 .319375 .277500
.234375 .190000 .144375 .097500 .049375
.000000

Approximate solution:

.988767 .988767 .988576 .987790 .986477
.984712 .981902 .974724 .963316 .951637
.939958 .928279 .916600 .896694 .876788
.856882 .836975 .814705 .791996 .769288
.746579 .723870 .701114 .676169 .647221
.616290 .581252 .545292 .508441 .469801
.430246 .390691 .351135 .311580 .272024
.232469 .192914 .150570 .108227 .065883
.023540

Right side error square : .000000D+00
Discrepancy : .207510D-06
Number of iterations : 400
Return code (IERR) : 0

Fig 4.8
=======



00001 IMPLICIT REAL*8(A-H,O-Z)
00002 IMPLICIT INTEGER*4(I-N)
00003 DIMENSION U0(41),Z(41),U(41,260),Z0(41)
00004 EXTERNAL AK
00005 X1=0.
00006 X2=1.
00007 Y1=-2.
00008 Y2=2.
00009 N=41
00010 M=41
00011 IMAX=100
00012 IC=1
00013 DL=0.
00014 C2=1.
00015 DO 1 J=1,N
00016 X=X1+(X2-X1)/(N-1.)*(J-1.)
00017 1 Z0(J)=1.-X*X
00018 CALL PTICR0(AK,U,X1,X2,Y1,Y2,N,M)
00019 CALL PTICR3(U,Z0,U0,N,M)
00020 DO 4 J=1,N
00021 Z(J)=0.5
00022 4 CONTINUE
00023 CALL PTILR(AK,U0,X1,X2,Y1,Y2,N,M,Z,AN,
*DL,ITER,IMAX,C2,IC,U,41*260,IERR)
00024 PRINT 5,Z0,Z,DL,AN,ITER,IERR
00025 STOP
00026 5 FORMAT(15X,'Exact solution:'/'.'/
* 8(5F11.6/),F11.6/'.'/
*15X,'Approximate solution:'/'.'/
* 8(5F11.6/),F11.6/'.'/
*10X,'Right side error square :',
* D14.6/
*10X,'Discrepancy :',
* D14.6/
*10X,'Number of iterations :',
* I14/
*10X,'Return code (IERR) :',
* I14)
00027 END


00001 FUNCTION AK(X,Y)
00002 IMPLICIT REAL*8(A-H,O-Z)
00003 IMPLICIT INTEGER*4(I-N)
00004 AK=1./(1.+100.*(X-Y)**2)
00005 RETURN
00006 END





Exact solution:

1.000000 .999375 .997500 .994375 .990000
.984375 .977500 .969375 .960000 .949375
.937500 .924375 .910000 .894375 .877500
.859375 .840000 .819375 .797500 .774375
.750000 .724375 .697500 .669375 .640000
.609375 .577500 .544375 .510000 .474375
.437500 .399375 .360000 .319375 .277500
.234375 .190000 .144375 .097500 .049375
.000000

Approximate solution:

1.000000 .999382 .997406 .994848 .989138
.983531 .983531 .961528 .961528 .948344
.948344 .912060 .912060 .894492 .894492
.835698 .835698 .835698 .808443 .752639
.752639 .728142 .728142 .628439 .628439
.609002 .584398 .584398 .584398 .386254
.386254 .386254 .386254 .361675 .307676
.183705 .183705 .159545 .095421 .048805
.000000

Right side error square : .000000D+00
Discrepancy : .442992D-15
Number of iterations : 100
Return code (IERR) : 3