"CODE" 33066;
"PROCEDURE" ARKMAT( T, TE, M, N, U, DER, TYPE, ORDER, SPR, OUT);
"VALUE" M,N,TYPE,ORDER;
"INTEGER" M,N,TYPE,ORDER;
"REAL" T,TE,SPR;
"ARRAY" U;
"PROCEDURE" DER,OUT;

"BEGIN" "INTEGER" SIG,L;
    "REAL" TAU;
    "ARRAY" LAMBDA[1:9],UH,DU[1:N,1:M];
    "BOOLEAN" LAST;

    "PROCEDURE" ELMMAT(A,B,X); "VALUE" X; "ARRAY" A,B; "REAL" X;
    "FOR" L:=1 "STEP" 1 "UNTIL" M "DO" ELMCOL(1,N,L,L,A,B,X);

    "PROCEDURE" INITIALIZE;
    "BEGIN" "INTEGER" I;"REAL" LBD;
    "SWITCH" TYPEODE:=NOTSPECIFIED2,PARABOLIC1,PARABOLIC2,HYPERBOLIC2;

    "IF" TYPE^=2 "AND" TYPE^=3 "THEN" TYPE:=1;
    "IF" TYPE^=2 "THEN" ORDER:=2 "ELSE" "IF" ORDER^=2 "THEN" ORDER:=1;
    I:=1;
    "GOTO" TYPEODE["IF" TYPE=1 "THEN" 1 "ELSE" TYPE+ORDER-1];

    NOTSPECIFIED2: "FOR" LBD:=1/9,1/8,1/7,1/6,1/5,1/4,1/3,1/2,4.3 "DO"
                   "BEGIN" LAMBDA[I]:=LBD; I:=I+1 "END";
                   "GOTO" EXIT;

    PARABOLIC1:    "FOR"LBD:=.1418519249"-2,.3404154076"-2,.0063118569
                              ,.01082794375,.01842733851,.03278507942,
                              .0653627415,.1691078577,156 "DO"
                   "BEGIN" LAMBDA[I]:=LBD; I:=I+1 "END";
                   "GOTO" EXIT;

    PARABOLIC2:    "FOR" LBD:=.3534355908"-2,.8532600867"-2,.015956206
                              ,.02772229155,.04812587964,.08848689452,
                              .1863578961,.5,64 "DO"
                   "BEGIN" LAMBDA[I]:=LBD; I:=I+1 "END";
                   "GOTO" EXIT;

    HYPERBOLIC2:   "FOR" LBD:=1/8,1/20,5/32,2/17,17/80,5/22,11/32,1/2,
                              8 "DO"
                   "BEGIN" LAMBDA[I]:=LBD; I:=I+1 "END";
                   "GOTO" EXIT;
    EXIT: SIG:=SIGN(TE-T)

    "END" INITIALIZE;

   "PROCEDURE" DIFFERENCE SCHEME;
   "BEGIN" "INTEGER" I;"REAL" MLT;

       DER(T,U,DU);
       "FOR" I:=1 "STEP" 1 "UNTIL" 8 "DO"
       "BEGIN" MLT:=LAMBDA[I]*TAU;
          DUPMAT(1,N,1,M,UH,U);
          ELMMAT(UH,DU,MLT);
          DER(T+MLT,UH,DU)
       "END";
       ELMMAT(U,DU,TAU);
       T:="IF" LAST "THEN" TE "ELSE" T+TAU;
    "END" DIFFERENCE SCHEME;

    INITIALIZE; LAST:="FALSE";

    STEP:
    TAU:=("IF" SPR=0 "THEN" ABS(TE-T) "ELSE" ABS(LAMBDA[9]/SPR))*SIG;
    "IF" T+TAU >= TE "EQV" TAU>=0 "THEN"
    "BEGIN" TAU:=TE-T;LAST:="TRUE" "END";
    DIFFERENCE SCHEME ; OUT;
    "IF" "NOT" LAST "THEN" "GOTO" STEP

"END" ARKMAT;
        "EOP"