How can I draw inside this for loop in maple?

Question

I have this code for Runge-Kutta-Fehlberg Method

while flag = 1 do k1 := h*f(t, w); k2 := h*f(t+(1/4)*h, w+(1/4)*k1); k3 := h*f(t+(3/8)*h, w+(3/32)*k1+(9/32)*k2); k4 := h*f(t+(12/13)*h, w+(1932/2197)*k1-(7200/2197)*k2+(7296/2197)*k3); k5 := h*f(t+h, w+(439/216)*k1-8*k2+(3680/513)*k3-(845/4104)*k4); k6 := h*f(t+(1/2)*h, w-(8/27)*k1+2*k2-(3544/2565)*k3+(1859/4104)*k4-(11/40)*k5); R := abs((1/360)*k1-(128/4275)*k3-(2197/75240)*k4+(1/50)*k5+(2/55)*k6)/h; if R <= Tol then t := t+h; w := w+(25/216)*k1+(1408/2565)*k3+(2197/4104)*k4-(1/5)*k5; y := subs(T = t, exact(T)) end if; printf(" %4.7f %4.7f %7.7f %7.7f\n", h, t, w, y); q := .84*(Tol/R)^(1/4); if q <= .1 then h := .1*h elif q >= 4 then h := 4*h else h := q*h end if; if h > hmax then h := hmax end if; if t >= b then flag := 0 elif t+h > b then h := b-t elif h < hmin then flag := 0 end if end do;

Now, I want to draw the values of y and w against t. I can't use seq plot because I don't have for loop. In Mathlab we usually open a file and then draw from the data. Here I couldn't do the same thing.

Answer 1

Maple creates a plot all at once, rather than building it incrementally. What you can do is build up the sequence of points, then plot it. Thus at the start:

tvalues:= NULL;
xvalues:= NULL;
yvalues:= NULL;

Then when you have computed t,x,y:

tvalues:= tvalues, t;
xvalues:= xvalues, x;
yvalues:= yvalues, y;

and after the loop finishes, something like:

npoints:= nops([tvalues]):
plot([[seq([tvalues[i],xvalues[i]],i=1..npoints)],
      [seq([tvalues[i],yvalues[i]],i=1..npoints)]], colour=[red,blue]);