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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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