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