Programming question: Iterative solution

• To: mathgroup at smc.vnet.net
• Subject: [mg22877] Programming question: Iterative solution
• From: "J.Guillermo Sanchez" <guillerm at gugu.usal.es>
• Date: Mon, 3 Apr 2000 00:04:08 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Friend, I have an iterative problem

Given the list:

In[1]:=
list1 = {1.90, 3.625, 5.18, 6.59, 7.87, 9.02, 10.07, 11.01, 11.87, 12.64};

and the equation (besed on trapezoid approximation for an integral)

In[2]:=
f[n_Integer] :=
Simplify[Sum[g[j - 1]*i[n - j + 1] + g[j]*i[n - j], {j, 1, n}] /. g[0] -> 0]

where

In[3]:=
g[n_Integer] := E^(-0.1*n) /; n > 0

I would like find the solution for any i[n]. I have precedured as follow

In[4]:=
sol[n_Integer] := Solve[f[n + 1] == Extract[list1, n + 1] , i[n]]

Now,  I can find the solution . E.g.

In[5]:=
sol[0]

Out[5]=
{{i[0] -> 2.09982}}

In[6]:=
sol[1] /. sol[0]

Out[6]=
{{{i[1] -> 1.05312}}}

In[7]:=
sol[2] /. sol[1] /. sol[0]

Out[7]=
{{{{i[2] -> 1.04989}}}}

But I thing is not to good method,

Can any body give me a more elegant solution?. Thanks

```

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