DDGE(3).mw

After "playing" with it one can reduce it to 5 equations and 5 variables

PS: the variable Epsilon1 is puzzling, it prints as E1 ... umpf.

May be you want to say a bit about your environment, seetings and commands.

For me following works (M18 32 bit on Intel Win 7 64 bit, classical interface):

p:= plot(exp): # no semi colon
plots[display](p);

For reasons of privacy I would have deleted the complete name. There is no need at all to publish it.

for that lame kind of question the answer is 1) RTFM and 2) probably the answer is 42

1. I always (hm ...) use backup functionality of Win and would prefer Maple to generate a re-entry point before install

2. Win 10? I will avoid it like the plaque, as far as possible, https://www.microsoft.com/en-us/privacystatement/default.aspx

Thx! I was not aware of that.

I think you want (D@@4)(f0)(S)=0; dsolve({%,bcs0});

But it makes no sense to say f = 1 and f(0) = 0

I think you want to iterate it until you are done

  Int(lambda(x)*(diff(y(x), x$3)), x): convert(%, D);
  Parts(%,         lambda(x)): convert(%, D);
  Parts(%, (D@@1)(lambda)(x)); #convert(%, D);
  Parts(%, (D@@2)(lambda)(x)); #convert(%, D);
 
                      /
                     |              (3)
                     |  lambda(x) (D   )(y)(x) dx
                     |
                    /


                  (2)
      lambda(x) (D   )(y)(x) - D(y)(x) D(lambda)(x)

                                      /
                  (2)                |         (3)
         + y(x) (D   )(lambda)(x) -  |  y(x) (D   )(lambda)(x) dx
                                     |
                                    /

Your sheet contains the same for n=5 instead of n=2. For me it works, but you seem to have version 13.

May be the following does it for you as well:

  diff(y(x), x$(n+1)): 
  convert(%, D): # change the notation
  
  Int(lambda(x)* %, x);
  Parts(%, lambda(x));

                    /
                   |              (n + 1)
                   |  lambda(x) (D       )(y)(x) dx
                   |
                  /


                                /
       (n)                     |    (n)        /d           \
     (D   )(y)(x) lambda(x) -  |  (D   )(y)(x) |-- lambda(x)| dx
                               |               \dx          /
                              /

I do not think that it would be easy to let Maple execute Excel code, which
is what you suggest. And named ranges can be arbitrarily complicated.

For that 2 ways come to my mind: either export and load. Or if ranges are
simple then feed a sheet to hold data in rows, first column = name, thus
a list of tables. At least you have to be able solve that first and may
try to solve it with 1 column (numerical values only, country setting =?),
naming for example "data_for_mpl".

Generally I think "bridging" completely different systems with different
goals is not an easy thing, leaving maintenance aside.

For me the approach works without 'double' simplify, Maple 18:

  assume( Tref > 0, Tsys > Tref, C3 > 0, C5 > 0);
  Int(ee, T=Tref..Tsys); 
  Expand(%); # each summand (avoiding bad simplification ?!)
  value(%);
  desired - %; convert(%, exp): simplify(%); #simplify(%, size);

                               0

Ok, that does not solve the task to have it in desired form (but
why you want that a priori?)

The 'only' thing is, that the result of pdsolve is not quite handy. After that one arrives at a function f, which is purely numeric (returning floats) and not analytic.

So your last question actually is towards "how Maple can integrate that?".

The syntax is given in the answer.

Usually Maple uses an adaptive way - and not a 'global' polynomial approximation - controlling the (guaranteed) error.

You can try Int(FF, 0 .. 1, method = _d01ajc); evalf(%); for a specific way, please read the help for those NAG routines (and you have to 'google' for details about 'adaptive Gauss-Kronrod method').

For your example you can ask Maple to find a global polynomial approximation - which I did using Tschebyshev polynomials. If you do so for the error 1e-10 then you get degree ~ 160 - which is useless in double precision.

In certain cases this method will not work (for example highly oscillating integrands or bad derivatives). The syntax given lets Maple decide which way to go.

NB: I always use Digits:= 15. The result may also depend on your time step (and much less on how Maple finds the integral). Just try the same with timestep = 0.1e-4.

Carl was faster + has a solution, so I post as Reply

Please do avoid to open 3 threads for asking the same/similar question.

The model is = 1 - '(a*N((m1-x)/s1) + (1-a)*N((m2-x)/s2))', and I guess you want 0 < s1, s2.

Note that you have to scale your data between 0 and 1, due to the model for x --> +- oo

Also be aware that your data beyond x=130 would not make sense (except you have a reason to do - they are the limit.

Now I would suggest to search for mixed distribution and how to estimate.

I think (!) that this also means to study the 'geometry' of the data graph and relate it to what you 'see'.

Do not expect too much: you only have 0 < x and the data seem to be disturbed a lot. Or is it true, that they may be *not* strictly increasing? Then you want to use that information for further analysis. That *may* indicate information for the means m1, m2.

For x=0 the model is almost zero. Solving for a guess one could start at 1/a = 1/a = 1-1/erfc(1/2*2^(1/2)*m2/s2)*erfc(1/2*2^(1/2)*m1/s1).

For plotting one does not need the equation for the inverse, one just reflects at the diagonal and displays that (sorry, I do not have the command at hand).

The paper has the code, but it is a different one

http://ecee.colorado.edu/~mcleod/teaching/nmip/hw/HW%201%20solution/project1.pdf