It doesn't look iterative. Anyway, one can interpolate B as a function of Y, then find solutions for given values of A, and interpolate them for corresponding values of t. For example, using splines,

t:= [ 0.05,0.1,0.2,0.5,1,2,5,10];
A:=[0.9,0.75,0.6,0.2,0.08,0.06,0.051,0.05];
Y:=[25,50,75,100,125,150,175,200,225,400,500,700,1000];
B:=[3250,2500,2000,1725,1550,1400,1325,1275,1225,950,850,775,775];
b:=unapply(CurveFitting:-Spline(Y,B,y),y);
R:=[seq(fsolve(y=A[i]*b(y)),i=1..nops(A))];
sol:=unapply(CurveFitting:-Spline(t,R,T),T);

The result doesn't look very nice though, see

plot(sol,0..10);

Alec

Thank u all so much for your suggestions.

Robert, for A(t) i would expect a double exponential : A = a*exp(-t/b)+c*exp(1/(t+d)) and   for B(Y) maybe : B=f*exp(-g*Y)+k

Ive tried to fit the data similarily the way u showed me but i must be doing something wrong. 1)  Could u please help me with that? in your example are the numebrs for d,e,f,g random values?

I have worked out these equations in the past but im not sure how they compare with wht u suggest if they are of any help:

For A=1.027*exp(-t/(.282))+0.051*exp(1/(t+1.766*10^90))   [1]

and B=2.433*10^3*exp(-0.008*Y)+780  [2]       but still my results are a bit off from wht they should be.

2) For A(t) i have almost 100 points in an excel file. Is there a simple way to enter this data in maple or do I have to type them in the Adata/Tdata format as above?

3) If u plot yf as shown below ( X axis log) for t=0.038 there is a small discontinouity. It happens even if i substitute [1], [2] in   Y=A(t) *B(Y) but only in maple. Any ideas why?

> with(Optimization); Tdata := [0.5e-1, .1, .2, .5, 1, 2, 5, 10]; Adata := [.9, .75, .6, .2, 0.8e-1, 0.6e-1, 0.51e-1, 0.5e-1]; TAdata := zip(`[]`, Tdata, Adata); Ydata := [25, 50, 75, 100, 125, 150, 175, 200, 225, 400, 500, 700, 1000]; Bdata := [3250, 2500, 2000, 1725, 1550, 1400, 1325, 1275, 1225, 950, 850, 775, 775]; YBdata := zip(`[]`, Ydata, Bdata);
> LSSolve([seq(a*exp(-b*t[1])+c-t[2], t = TAdata)], a = 0 .. 2, b = 0 .. 10, c = 0 .. 0.05); abcsol := %[2];
> LSSolve([seq(d*t[1]^e+f*t[1]^g-t[2], t = YBdata)], initialpoint = [d = 61875, e = -1, f = 775, g = 0]); defgsol := %[2];
Warning, limiting number of iterations reached
>
> yf := proc (t) options operator, arrow; fsolve(eval(y = (a*exp(-b*t)+c)*(d*y^e+e*y^f), {op(abcsol), op(defgsol)}), y = 0 .. 1000) end proc;
> yf(1);
127.3895493
> plot(yf, 0.01 .. 10, axis[1] = [mode = log], labels = [t, y]);
 

Thanks in advance for your time.

ExcelTools:-Import can be used for importing data from Excel.

Alec