The code works fine for me

tt = Table[{g, qQnum[g]}, {g, 0, Ts}]
(*
{{0, 0.303553}, {1, 0.299951}, {2, 0.296613}, {3, 0.293514},
 {4, 0.290635}, {5, 0.287959}, {6, 0.285475}, {7, 0.283173},
 {8, 0.281044}, {9, 0.279083}, {10, 0.277284}, {11, 0.275644},
 {12, 0.27416}}
*)

ListLinePlot[tt]

Hello Vedat, I am afraid I do not understand what you mean. What do you mean by "one gets the value of x[t] versus G" ? x[t] is a function and not a value! x[ .85 ] for example is a value, and this value certainely depends on G. But for a given t x[ t ] is a linear function of G (look for example at fx[.1, g] ), so you get a straight line. The same is true for y, I attach some code which shows how the functions x[t] and y[t] ( and not a value ) change with G (in my code g)

eq1 = x'[t] == y[t];
eq2 = y'[t] == 6 x[t] - y[t] + g;
sol = DSolve[{eq1, eq2, x[0] == 0, y[0] == 1}, {x, y}, t];
fx[t_, g_] := Evaluate[(x /. sol[[1, 1]])[[2]]]
fy[t_, g_] := Evaluate[(y /. sol[[1, 2]])[[2]]]
(* Show x[t] depending on g  *)
Manipulate[
 Plot[fx[tt, g], {tt, 0, 2}, PlotRange -> {0, 6}],
 {g, 0, 1}]
(* Show both x[t] (red) y[t] (blue)  depending on g  *)
Manipulate[
 Plot[{fx[t, g], fy[t, g]}, {t, 0, 2},
  PlotRange -> {0, 6},
  PlotStyle -> {Red, Blue}],
 {g, 0, 1}]
(* Show the vector { x[t], y[t] } depending on g  *)
Manipulate[
 ParametricPlot[{fx[t, g], fy[t, g]}, {t, 0, 2},
  PlotRange -> {{0, 2}, {0, 4}}],
 {g, 0, 1}]

Horner seems to be about 10% faster (at least on my machine). And you should change all variables with super and/or subscripts or both.

cc = RandomReal[{1, 10}, 6]
p1 = Sum[cc[[i]] x^(i - 1), {i, 1, Length[cc]}]
p2 = HornerForm[p1]


Timing[
 Do[
  e1 = p1 /. x -> .245,
  {i, 100000}];
 e1]

Out[47]= {0.858, 5.16398}


Timing[
 Do[
  e2 = p2 /. x -> .245,
  {i, 100000}];
 e2]

Out[48]= {0.749, 5.16398}

Hello Vedat,

a pdf is not really better than a foto. No chance to run or edit it. And I am afraid I really can't speed up your code. For me it is too complicated in fact.

Some general remarks: you should avoid variables starting with a capital letter. Such a variable could be an internal symbol. You don't get an error, but results are not what you expect. So: no captial letters. You should avoid variables with super- and/or subscripts, or both. As far as I remember it occurred sometimes that they were not handled in the way you want to.

You should analyze your sums. Are there constants common to some sums and could they be calculated once and outside the sum? I noticed there are power-sums: rewrite them according to Horner's scheme.

And are you sure your

Do[ For [....

constructs is really what you want?

Greetings, Hans

Hello Hans, Possibly there is some mistyping errors. So, thank you for your help. Vedat. Take care.

@ Rohit

Hello Rohit, thank you for your answer. " I believe you are running V8? " It is even worse, I am very old fashioned and only have V 7. So this is my situation: NDSolve gave solutions for x[t] and y[t], but NIntegrate gave some errors, and so it is very likely that my qQnum is wrong. And I couldn't reproduce any of the pics in the paper, what seems to be what Vedat wants to do.

I can not get the same result Could you please as a single code again?

Hello Hans, According to the paper, n=1,2,3,...,T=2Pi/w and Ts=nT. I have added them to the code. But I can not run it.I need your help.

Attachments:

Bel1.pdf

Hmmmm ?

Ok, add to the foregoing code this (but there seems to difficulties during the integration, I didn't have a closer look at this) It doesn't look similar to fig. 4c.

qQnum[g_] := Module[{},
  nT = 10;
  lsg = sol[g, nT];
  fx = x /. lsg[[1, 1]];
  fy = y /. lsg[[1, 2]];
  qQs = NIntegrate[fx[t] (Sin[w t] /. val), {t, 0, nT}] 2/nT;
  qQs = NIntegrate[fx[t] (Sin[w t] /. val), {t, 0, nT}] 2/nT;
  qQc = NIntegrate[fx[t] (Cos[w t] /. val), {t, 0, nT}] 2/nT;
  qnum = Sqrt[qQs^2 + qQc^2]]

and

tt = Table[{qQnum[g], g}, {g, 0, 200}];
ListLinePlot[tt]
ListLinePlot[Reverse /@ tt]

Hello again Hans; Please see the attached files for my parameters.we can use them to get for example figure 4 c.&By the way, in your eq11b lam^2 x^4 should be replaced with lam^2 x^5Wolfram Notebook

Attachments:

parameters.pdf