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Re: calculate Recurrence Equations


Add memory to the definition

Clear[anteil1];
anteil1[0]=1;
anteil1[n_Integer?Positive]:=
    anteil1[n]=
      anteil1[n-1]+(anteil1[n-1]*5-1)/100;
anteil1[n_Integer?Negative]:=
    anteil1[n]=(1/105)*(100*anteil1[n+1]+1);

anteil1[30]//Timing//N

{0.002837 Second,3.65755}

Clear[anteil2];

anteil2[n_]=anteil2[n]/.RSolve[{
          anteil2[n]==anteil2[n-1]+(anteil2[n-1]*5-1)/100, 
          anteil2[0]==1},anteil2[n],n][[1]]

(1/5)*(1 + 4^(1 - n)*(21/5)^n)

anteil2[30]//Timing//N

{0.000229 Second,3.65755}

Plot[anteil2[n],{n,-10,10},
    PlotStyle->Blue,ImageSize\[Rule]432,
    Epilog->{Red, AbsolutePointSize[4],
        Point/@Table[{n,anteil1[n]},{n,-10,20}]}];


Bob Hanlon

---- Frank Hechtner <frank.hechtner at rub.de> wrote: 
> hi,
> 
> i?m in trouble with my Recurrence Equations:
> 
> i?ve defined the following function
> 
> anteil[0] = 1
> anteil[n_] := anteil[n - 1] + (anteil[n - 1]*5 - 1)/100
> 
> i want mathematica to calculate the values for anteil[30] and so on.
> 
> Unfortunately mathematica needs for this calculation over 2 hours (and 
> is still running, athlon x2 4600, 2 gb ram).
> 
> I don?t see where are the difficulties for mathematica...
> 
> Thanx for your help
> 
> frank
> 


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