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Series solutions to nonlinear ODES and ODEs (new automated method)

Posted 3 years ago
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Hi,

We have a question: Is there a channel that innovators can use to approach the makers of Mathematica (Wolfram Research Inc.), to present new discoveries? Mathematica was an essential tool in my own PhD work and I always regard them as being open to suggestion of improving their computational routines.

We recently have come up with a new fully automated method for finding series solutions to wide classes of nonlinear ODEs and PDEs, opening new horizons in approaching DEs. We posted our results in a Facebook page: https://www.facebook.com/nonlinearDE. We have also written a document in reply to their request to specify the type of PDEs ODEs we can solve. See the first two links provided, the first one is the document and second one is solutions to two examples in the first document. see the document and supplement to it. We also include a copy of slides the in the FB page, not very tidy but one may want to see that, rather than the FB pagePdf version of examples. These links are also available in the FB page.

Where we found Maple was much more open to be approached (recognizing the importance of the work, they got engaged with us and started to evaluate our work for possible inclusion in their product), we found WRI extremely closed to outside their network. We found it impossible to find someone to at least have a look at our work. This shouldn't be this difficult.

We are a bit disappointed with the situation, we always regarded Mathematica very highly and considered it an integral part of the scientific and engineering community; however, we are feeling like character K. in Kafka's novel "The Castle" ; we now its there but there is no way to get in]

We are just wondering whether there is a channel that people like us can communicate with WRI. We just couldn't find it.

We would appreciate it if you can refer us to someone who we could talk to. Thank you.

Regards, Amin

2 Replies

Already there is ,a commercial solutions in the form of an additional package.

Posted 3 years ago

First of all we solve nonlineat DES and system of DEs not specifically linear,LDE, as that package suggest. Solving linear des are easy to do. 2- We do not approximate solution by polynomials, some it might look have a form of polynomials but not all, we provide coverging series solution. The polynomial does not work for many problems like wave and vibration problem. Have a look at the vibration problem and KDV in our examples. They could never solve those. 3- Have a look at the documents I have provided and and see what a wide range of equations we cover.

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