I would like to solve equations, but I got some errors.

Dear Matlab experts,

My coding is below, and I would like to get t. Please let me know how to solve this problem.

Thank you very much in advance.

Sincerely yours,

R

z = 17267.895; a = - 7354.746; b = - 1881.38; c = - 4032.548; d = - 2814.639; e = - 3915.966; f = - 4932.209; g = - 3241.126; h = - 7162.355; aa = 34126547; bb = 1337705000; cc = 81776930; dd = 60483385; ee = 127450459; ff = 142389000; gg = 62271177; hh = 309326225; i = aa*exp(-t.*a) + bb*exp(-t.*b) + cc*exp(-t.*c) + dd*exp(-t.*d) + ee*exp(-t.*e) + ff*exp(-t.*f) + gg*exp(-t.*g) + hh*exp(-t.*h); j = (aa*exp(-t.*a))./i; k = (bb*exp(-t.*b))./i; l = (cc*exp(-t.*c))./i; m = (dd*exp(-t.*d))./i; n = (ee*exp(-t.*e))./i; o = (ff*exp(-t.*f))./i; p = (gg*exp(-t.*g))./i; q = (hh*exp(-t.*h))./i; jj = z*j; kk = z*k; ll = z*l; mm = z*m; nn = z*n; oo = z*o; pp = z*p; qq = z*q; r = 499.137372; rr = 8286.891952; s = 745.383756; ss = 406.307267; u = 1170.715419; uu = 1740.776238; v = 493.50486; vv = 5433.056536; x = r + rr + s + ss + u + uu + v + vv; w = z*r/x; ww = z*rr/x; y = z*s/x; yy = z*ss/x; zz = z*u/x; tt = z*uu/x; ab = z*v/x; cd = z*vv/x; solve ((bb*exp(-t*b))/i == rr/x , t)

[Image Analyst]

http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup

[Walter Roberson]

What errors do you get?

Answer 1

[Walter Roberson]

When I pushed it through the MATLAB -> Maple interface, it complained that the exponents were too large to solve. When I copied over the floating point form of the expression to be solved to Maple, the same error occurred.

I then copied into Maple and edited to get Maple syntax, and along the way converted each floating point number to rational. The MATLAB MuPAD-based symbolic engine by default converts each floating point number to rational as the floating point number gets involved in a symbolic expression, but when floating-floating operations are done before the expression is entangled with a symbol, floating point results are calculated. To get the same effect in MuPAD you would have to sym() each of the floating point numbers as you went.

Having transcribed into Maple, I started Maple towards solving it. After it had proceeded for a moment I realized the complexity of the expression and knew that Maple would take a long time on it, as Maple would be trying to find an exact solution. I then interrupted Maple, plotted the function over a limited range, narrowed in on a portion of the range, and asked Maple to find a numeric solution within that range. The result was that the solution is 0.000195281103070472

For the record, the Maple code version become:

Q := v -> convert(v, rational);
z := Q(17267.895);
a := Q(-7354.746); 
b := Q(-1881.38); 
c := Q(-4032.548); 
d := Q(-2814.639); 
e := Q(-3915.966); 
f := Q(-4932.209); 
g := Q(-3241.126); 
h := Q(-7162.355); 
aa := Q(34126547); 
bb := Q(1337705000); 
cc := Q(81776930); 
dd := Q(60483385); 
ee := Q(127450459); 
ff := Q(142389000); 
gg := Q(62271177); 
hh := Q(309326225); 
i := aa * exp(-t*a) + bb * exp(-t*b) + cc * exp(-t*c) + dd * exp(-t*d) + ee * exp(-t*e) + ff * exp(-t*f) + gg * exp(-t*g) + hh * exp(-t*h); 
j := aa*exp(-t*a)/i; 
k := bb*exp(-t*b)/i; 
l := cc*exp(-t*c)/i; 
m := dd*exp(-t*d)/i; 
n := ee*exp(-t*e)/i; 
o := ff*exp(-t*f)/i; 
p := gg*exp(-t*g)/i; 
q := hh*exp(-t*h)/i; 
jj := z*j; 
kk = z*k; 
ll := z*l; 
mm := z*m; 
nn := z*n; 
oo = z*o; 
pp := z*p; 
qq := z*q; 
r := Q(499.137372); 
rr := Q(8286.891952); 
s := Q(745.383756); 
ss := Q(406.307267); 
u := Q(1170.715419); 
uu := Q(1740.776238); 
v := Q(493.50486); 
vv := Q(5433.056536); 
x := r+rr+s+ss+u+uu+v+vv; 
w := z*r/x; ww := z*rr/x; 
y := z*s/x; 
yy := z*ss/x; 
zz := z*u/x; 
tt := z*uu/x; 
ab := z*v/x; 
cd := z*vv/x;
fsolve(bb*exp(-t*b)/i - rr/x, t=-1/1000..1/1000)

[Redwood]

Dear Walter Roberson,

Thank you very much for your help.

After I put this coding, I got this message from Matlab.

"Undefined function 'Q' for input arguments of type 'char'."

I think my Matlab itself has some problem, what do you think?

Sincerely yours,

R

[Walter Roberson]

The code I show above is Maple code, not MATLAB code. The closest you would get would be to open a MuPAD notebook and paste the code there. I believe the command to open a MuPAD notebook is

notebook

MuPAD's method of converting to rational looks different. In MuPAD you would have to replace

Q := v -> convert(v, rational);

with something like

Q := v -> coerce(v, DOM_RAT);

You might also have to replace

   fsolve(bb*exp(-t*b)/i - rr/x, t=-1/1000..1/1000)

with

numeric::solve(bb*exp(-t*b)/i - rr/x, t=-1/1000..1/1000)