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Re: NDSolve output without interpolating function

• To: mathgroup at smc.vnet.net
• Subject: [mg124332] Re: NDSolve output without interpolating function
• From: "Scot T. Martin" <smartin at seas.harvard.edu>
• Date: Tue, 17 Jan 2012 03:24:10 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201201150952.EAA19696@smc.vnet.net>,<201201162209.RAA15364@smc.vnet.net>

Another "wow" from me. I hope the right person at Wolfram is listening. It would be really great to know about this additional functionality for NDSolve within its documentation, which is a great function that I have been using since 1994 (flattery to Wolfram!) and for which I am very keen to now learn about these additional possibilities (petition to Wolfram!). Please.


________________________________________
From: Oliver Ruebenkoenig [ruebenko at wolfram.com]
Sent: Monday, January 16, 2012 17:09
To: mathgroup at smc.vnet.net
Subject: [mg124332] Re: NDSolve output without interpolating function

On Sun, 15 Jan 2012, Oleksandr Rasputinov wrote:

> On Sat, 14 Jan 2012 22:21:47 -0000, Nasser M. Abbasi <nma at 12000.org> wrote:
>
>> On 1/14/2012 2:01 AM, Oliver Ruebenkoenig wrote:
>>> On Fri, 13 Jan 2012, william cuervo wrote:
>>>
>>>> Hi!
>>>>
>>>> Is there any way that NDSolve presents the output as a set of data
>>>> instead
>>>> of as an interpolating function?
>>>>
>>>>
>>>> Thanks!
>>>>
>>>
>>> Hi,
>>>
>>> how about
>>>
>>> s = y /. First@
>>>      NDSolve[{y'[x] == y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}]
>>>
>>> s["ValuesOnGrid"]
>>>
>>> s["Methods"]
>>>
>>> Oliver
>>>
>>
>> Wow, that is amazing. Never knew about these. Any idea where to
>> read more about these options? to understand more what they return
>> and such.
>>
>> Sounds like they will be very useful to know about. nothing in
>> documentation
>> center on them.
>>
>> thanks
>> --Nasser
>>
>
> These have a rather unusual form of documentation that works as follows:
>
> s["MethodInformation"["ValuesOnGrid"]]
>
> prints:
>
> System`InterpolatingFunction`ValuesOnGrid
>
> InterpolatingFunction[domain, data]@ValuesOnGrid[] gives the function
> values at each grid point.  In some cases, this may be faster than
> evaluating at each of the grid points.
>
> Attributes[System`InterpolatingFunction`ValuesOnGrid] = {Protected}
>
> Options[System`InterpolatingFunction`ValuesOnGrid] = {DropPeriodicEndpoint
> -> False}
>
> (of course, you can substitute "ValuesOnGrid" for whatever Method you are
> interested in.)
>
>


I filed a suggestion that the documentation on "MethodInformation" be
improved in the future.

In general, I usually, try "Properties" and "Methods" on objects. Some of
them offer additional functionality (while the one in this case can be
accessed via the anatomy package (tutorial/NDSolvePackages#120436095))


Thanks,
Oliver

• References:
  • Re: NDSolve output without interpolating function
    • From: "Oleksandr Rasputinov" <oleksandr_rasputinov@hmamail.com>
  • Re: NDSolve output without interpolating function
    • From: Oliver Ruebenkoenig <ruebenko@wolfram.com>