Fay

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13 years, 13 days

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These are replies submitted by Fay

Firstly thanks for your prompt reply! Secondly yes there is a missing minus sign, as the integral should be the Laplace transform of the function f(t). If my understanding is correct, it appears from the dominated convergence theorem that if f(t) is of exponential order and t > 0, then the exp(-s*t) term will dominate and therefore it will be permissible to take the limit through the integral. Is this correct?

Firstly thanks for your prompt reply! Secondly yes there is a missing minus sign, as the integral should be the Laplace transform of the function f(t). If my understanding is correct, it appears from the dominated convergence theorem that if f(t) is of exponential order and t > 0, then the exp(-s*t) term will dominate and therefore it will be permissible to take the limit through the integral. Is this correct?

Having now tried the built-in Mathematica to Maple converter, I can unfortunately confirm that it needs a lot more work done to it, before it is really useful. Sometime ago Mathematica did give away really useful reader for their notebooks, unfortunately their latest version seems to more bloatware than something useful.

Many Thanks!!!

This is an alternative version of Talbot's method, that is just a translation of Alex Potapchik's procedure

Talbot := proc (Fs, t, D)

local ctn, d, du, Gs, k, ft, p, r, theta, u, v;

  Digits := D;
  r := (2/5)*D/t;
  Gs := unapply(Fs, s);
  d := D-1; ft := 0;
  p := evalf(Pi/D);

  for k to d do
    theta := k*p;
    ctn := cot(theta);
    u := r*theta*ctn+I*r*theta;
    du := theta+theta*ctn^2-ctn;
    v := Gs(u)*exp(t*u);
    ft := ft+Re(v+I*v*du)
  end do;

  return (1/5)*(Gs(r)*exp(r*t)+2*ft)/t

end proc

Does anyone have a Maple version of any other methods, such as the GWR algorithm?

 

The test program has been optimised for both the Pascal compiler and for the Maple interpreter, in the latter case thru the use of hardware floats. As resutl of this both programs have been optimised for their software enviroments, however, I would not have expected such a large difference as the I have measured

I really want something small and portable that will run some version of Maple! As I own a copy of Maple V, I was thinking along the lines of a PDA, hence the reference to Casio. Alernatively, does anyone have any idea how well Maple 12 runs on a netbook with an Intel atom CPU.

Yep done all that, even had the tea as suggested, only problem is the files still do not appear to have uploaded!
As there appears to be a problem uploading the maple worksheet maybe this will work! > restart: > Zakian := proc(Fs,t) local a,k; if t = 0 then error("The approximation is undefined for the value t = 0") end if: a[1] := 12.83767675e0 + j*1.666063445e0: a[2] := 12.22613209e0 + j*5.012718792e0: a[3] := 10.93430308e0 + j*8.409673116e0: a[4] := 8.776434715e0 + j*11.92185389e0: a[5] := 5.225453361e0 + j*15.72952905e0: k[1] := -3.690208210e4 + j*1.969904257e5: k[2] := 6.127702524e4 - j*9.540862551e4: k[3] := -2.891656288e4 + j*1.816918531e4: k[4] := 4.655361138e3 - j*1.901528642e0: k[5] := -1.187414011e2 - j*1.413036911e2: return(2/t*add(Re(k[i]*eval(Fs,s = a[i]/t)),i = 1..5)) end proc: > f(t) := sin(4*t)*exp(-t); f(t) := sin(4 t)exp(-t) > F(s) := laplace(f(t),t,s); 4 F(s) := ------------- 2 s + 2 s + 17 > plot({f(t),Zakian(F(s),t)},t = 0.001..8);
If there is not a problem with the uploading mechcanism, perhaps someone can write a procedure on how to do it, as I have tried to upload this worksheet any number of times!
I have on a number of tried to upload the Maple Worksheet demonstrating Zakian's method of numerically inverting the Lapalce transform but the files seem to vanish! Is there a bug in the uploading routine? Please replace this text with the link to your file. The link can be found in the File Manager
Have you had a look at Zakian's Method of numericaly inverting Laplace transforms, quick, simple but does have its problems Please replace this text with the link to your file. The link can be found in the File Manager
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