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MathGroup Archive 2005

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A suggestion regarding Initial Conditions in ODEs.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57411] A suggestion regarding Initial Conditions in ODEs.
  • From: "Narasimham" <mathma18 at hotmail.com>
  • Date: Fri, 27 May 2005 04:56:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Initial conditions could be directly appended to the variable itself
being integrated when encountered for the first time. This could
shorten code by avoiding repetition of lower order derivative names. A
left directed arrow may indicate input initial values.
As an advantage,it could directly avoid errors due to mismatch between
number of constraints and number of total differential orders,as the
number of primes and number of initial arguments are placed/written
almost side by side for a quicker visual tally.

 E.g., a cosine curve could be coded as :

 NDSolve[y''[t]<-[0, 1] == -y[t], y, {t, 0, 2 Pi}] instead of

 NDSolve[{y''[t] == -y[t], y'[0] == 0, y[0] == 1}, y, {t, 0, 2 Pi}];

 The notation can be generalized to PDE. But, am not aware of other
connected systemic implications.

Regards,
Narasimham


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