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Re: NDSolve output without interpolating function


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.)



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