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   sci.math.symbolic      Symbolic algebra discussion      10,432 messages   

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   Message 8,958 of 10,432   
   Richard Fateman to All   
   Re: if result of dsolve contains integra   
   11 Jan 16 08:55:53   
   
   From: fateman@cs.berkeley.edu   
      
   There is an argument to be made that the numerical evaluation of an   
   explicit integral by some well-known, stable, efficient method may   
   be far preferable to the numerical evaluation of a complicated   
   non-integral expression involving special functions, perhaps   
   in an unstable fashion.   (Note in particular that if you are   
   computing F(b)-F(a)   for  a,b close together, you may be   
   looking at the small difference of large numbers = trouble).   
      
   There is the possibility of having extra parameters which make   
   quadrature impossible,   but for the common practice of taking   
   the result of an ode-solver and plotting, you may not have   
   extra parameters at all.  Or a plot with extra dimensions.   
      
   Also, it may be that the explicit solution of ODEs by numerical   
   methods is even better than finding an integral form and then   
   numerically evaluating the integral.   
      
   So the Kamke task per se may be more of a "we can do it" than   
   a "people really need this done, and isn't it great that we   
   can do it for them."   
      
   Rjf   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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