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DSolve question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88746] DSolve question
  • From: igwood <igwood at yahoo.co.jp>
  • Date: Thu, 15 May 2008 07:50:15 -0400 (EDT)

Hi everyone. I'm looking for help using the result of DSolve. 
In the code below the DSolve statements in In[3] and In[4] find i1[t] and i2[t] respectively in terms of variable t and a constant a1, a2 respectively. Then, numerical values for a1 and a2 will be found by simultaneous equations equating i1[t] and i2[t] in the FindRoot statement in In[7]. 
However, I havenâ??t been able to make Mathematica relate the i1[t], i2[t] in FindRoot to the i1[t], i2[t] resulting from DSolve. Iâ??ve tried several ways and finally the way below and always get errors. 
On the other hand if I COPY and PASTE the DSolve output Out[3], Out[4] following the -> into the lhs of i1[t] = lhs, then the FindRoot gives me the a1, and similar for a2.. 
If anyone can instruct me on how to get the FindRoot to recognize the i1[t], i2[t] found from DSolve I would appreciate it. I guess in other words, how do I get output of DSolve to be a usable function. 

In my own reply to this post I will paste the example of the code where COPY/PASTE has been used as described above to give numerical values for a1, a2.

Thanks in advance.


In[1]:= Duty = .6; SWfreq = 1*10^6; Vin = 3.2; Vout = 1.8; L = 
 4.7*10^-7; R = 0.008;

In[2]:= Dt1 = 
 Duty (1/SWfreq); Dt2 = (1 - Duty) (1/SWfreq); VL2 = - Vout; VL1 = 
 Vin - Vout; T = 1/SWfreq;

In[3]:= it1 = 
 Simplify[DSolve[{L i1'[t] + R i1[t] - VL1 == 0, i1[0] == a1}, i1[t], 
   t]]

Out[3]= {{i1[t] -> 175.+ (-175. + 1. a1) E^(-17021.3 t)}}

In[4]:= it2 = 
 Simplify[DSolve[{L i2'[t] + R i2[t] - VL2 == 0, i2[0] == a2}, i2[t], 
   t]]

Out[4]= {{i2[t] -> -225. + (225.+ 1. a2) E^(-17021.3 t)}}

In[5]:= i1[t_] = i1[t] /. it1

Out[5]= {175.+ (-175. + 1. a1) E^(-17021.3 t)}

In[6]:= i2[t_] = i2[t] /. it2

Out[6]= {-225. + (225.+ 1. a2) E^(-17021.3 t)}

In[7]:= FindRoot[{i1[0] == i2[T], 
  i1[Dt1] == i2[Dt1]},
 {a1, 0}, {a2, 0}]

During evaluation of In[7]:= Thread::tdlen: Objects of unequal length \
in {0,{-0.983123}}+{{1.,0}} cannot be combined. >>

During evaluation of In[7]:= Thread::tdlen: Objects of unequal length \
in {{1.,0}}+{0,{-0.983123}} cannot be combined. >>

During evaluation of In[7]:= Thread::tdlen: Objects of unequal length \
in {0,{-0.989839}}+{{0.989839,0}} cannot be combined. >>

During evaluation of In[7]:= General::stop: Further output of \
Thread::tdlen will be suppressed during this calculation. >>

During evaluation of In[7]:= FindRoot::njnum: The Jacobian is not a \
matrix of numbers at {a1,a2} = {0.,0.}. >>

Out[7]= {a1 -> 0., a2 -> 0.}


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