LISTING 1

In this extract A and B are previously declared constants 
with value 0.2928932 and 1.7071068 respectively. K Calc is 
a procedure for calculating the Ks from the various dYs/dt. 
The Rs and Qs are intermediate quantities to facilitate 
evaluation. The following segment is not offered as a model 
of programming, but to show clearly the procedure technique. 
Before executing it, the user is required to enter the initial 
conditions, i.e. the Ys starting values.

K_Calc; 
repeat
  FOR i:= 0 TO 4 DO 
  begin 
    R[i] := 0.5*K[i] - Q[i]; 
    Y[i] := Y[i] + R[i]; 
    Q[i] := Q[i] + 3.0*R[i] - 0.5*K[i]; 
  end; 
  K_Calc; 
  FOR i:= 0 TO 4 DO
  begin 
    R[i] := A*(K[i] - Q[i]);
    Y[i] := Y[i] + R[i];
    Q[i] := Q[i] + 3.0*R[i] - A*K[i];
  end; 
  K_Calc; 
  FOR i:= 0 TO 4 DO
  begin 
    R[i] := B*(K[i] - Q[i]); 
    Y[i] := Y[i] + R[i];
    Q[i] := Q[i] + 3.0*R[i] - B*K[i];
  end; 
  K_Calc; 
  FOR i:= 0 TO 40 DO
  begin 
    R[i] := (K[i] - 2.0*Q[i])/6.0; 
    Y[i] := Y[i] + R[i];
    Q[i] := Q[i] + 3.0*R[i] - 0.5*K[i];
  end; 
  K Calc; 
until ...