"CODE" 33180;
"PROCEDURE" DIFFSYS(X,XE,N,Y,DERIVATIVE,AETA,RETA,S,H0,OUTPUT);
"VALUE" N;
"INTEGER" N;
"REAL" X,XE,AETA,RETA,H0;
"ARRAY" Y,S;
"PROCEDURE" DERIVATIVE,OUTPUT;
"BEGIN" "REAL" A,B,B1,C,G,H,U,V,TA,FC; "INTEGER" I,J,K,KK,JJ,L,M,R,SR;
    "ARRAY" YA,YL,YM,DY,DZ[1:N],DT[1:N,0:6],D[0:6],YG,YH[0:7,1:N];
    "BOOLEAN" KONV,B0,BH,LAST;
    LAST:="FALSE"; H:=H0;
NEXT: "IF" H*1.1>=XE-X "THEN"
    "BEGIN" LAST:="TRUE"; H0:=H; H:=XE-X+"-13 "END";
    DERIVATIVE(X,Y,DZ); BH:="FALSE";
    "FOR" I:=1 "STEP" 1 "UNTIL" N "DO" YA[I]:=Y[I];
ANF: A:=H+X; FC:=1.5; B0:="FALSE"; M:=1; R:=2; SR:=3; JJ:=-1;
    "FOR" J:=0 "STEP" 1 "UNTIL" 9 "DO"
    "BEGIN" "IF" B0 "THEN"
        "BEGIN" D[1]:=16/9; D[3]:=64/9; D[5]:=256/9 "END"
        "ELSE" "BEGIN" D[1]:=9/4; D[3]:=9; D[5]:=36 "END";
        KONV:="TRUE";
        "IF" J>6 "THEN" "BEGIN" L:=6; D[6]:=64; FC:=.6*FC "END"
        "ELSE" "BEGIN" L:=J; D[L]:=M*M "END";
        M:=M*2; G:=H/M; B:=G*2;
        "IF" BH "AND" J<8 "THEN"
        "BEGIN" "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
            "BEGIN" YM[I]:=YH[J,I]; YL[I]:=YG[J,I] "END"
        "END"
        "ELSE"
                KK:=(M-2)/2; M:=M-1;
            "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
            "BEGIN" YL[I]:=YA[I]; YM[I]:=YA[I]+G*DZ[I] "END";
            "FOR" K:=1 "STEP" 1 "UNTIL" M "DO"
            "BEGIN" DERIVATIVE(X+K*G,YM,DY);
                "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
                "BEGIN" U:=YL[I]+B*DY[I]; YL[I]:=YM[I]; YM[I]:=U;
                    U:=ABS(U); "IF" U>S[I] "THEN" S[I]:=U
                "END";
                "IF" K=KK "AND" K^=2 "THEN"
                "BEGIN" JJ:=JJ+1; "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
                    "BEGIN" YH[JJ,I]:=YM[I]; YG[JJ,I]:=YL[I] "END"
                "END"
            "END"
        "END";
        DERIVATIVE(A,YM,DY);
        "FOR" I:=1 "STEP" 1 "UNTIL" N "DO"
        "BEGIN" V:=DT[I,0]; TA:=C:=DT[I,0]:=(YM[I]+YL[I]+G*DY[I])/2;
            "FOR" K:=1 "STEP" 1 "UNTIL" L "DO"
            "BEGIN" B1:=D[K]*V; B:=B1-C; U:=V;
                "IF" B^=0 "THEN"
                "BEGIN" B:=(C-V)/B; U:=C*B; C:=B1*B "END";
                V:=DT[I,K]; DT[I,K]:=U; TA:=U+TA
            "END";
            "IF" ABS(Y[I]-TA)>RETA*S[I]+AETA "THEN" KONV:="FALSE";
            Y[I]:=TA
        "END";
        "IF" KONV "THEN" "GOTO" END;
        D[2]:=4; D[4]:=16; B0:=^B0; M:=R; R:=SR; SR:=M*2
    "END";
    BH:=^BH; LAST:="FALSE"; H:=H/2; "GOTO" ANF;
END: H:=FC*H; X:=A; OUTPUT; "IF" "NOT" LAST "THEN" "GOTO" NEXT;
"END" DIFFSYS;
        "EOP"