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MathGroup Archive 2005

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DSolve with recursively defined equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53760] DSolve with recursively defined equations
  • From: pdickof at sasktel.net
  • Date: Wed, 26 Jan 2005 04:37:21 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

DSolve can handle this....
eq[0] = n0'[d] == -r n0[d];
eq[1] = n1'[d] == r(n0[d]  - n1[d]);
eq[2] = n2'[d] == r(n1[d]  - n2[d]);
in[0] = n0[0] == 1;
in[1] = n1[0] == 0;
in[2] = n2[0] == 0;
eqns = Flatten[Table[{eq[i], in[i]}, {i, 0, 2}]];
funcs = {n0[d], n1[d], n2[d]};
DSolve[eqns, funcs, d]

...but when I try to generalize to the following ...
Remove[nn, eq, in, eqns, funcs];
iCount=2;
eq[0] = nn'[0, d] == -r nn[0, d];
eq[i_] := nn'[i, d] == r(nn[i - 1, d]  - nn[i, d]);
in[0] = nn[0, 0] == 1;
in[i_] := nn[i, 0] == 0;
eqns = Flatten[Table[{eq[i], in[i]}, {i, 0, iCount}]];
funcs = Table[nn[i, d], {i, 0, iCount}];
DSolve[eqns, funcs, d]

...I get the message
DSolve::bvnul: For some branches of the general solution, \
the given boundary conditions lead to an empty solution.

I don't understand the difference. Is it possible to generalize as
above? Is it possible to obtain a general solution for the ith
equation? What are the relevant sections in the documentation?
Thanks in advance.....

Peter Dickof


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