>From few days I am trying to go through all the methods that I have
posted.N ow I have got all the basic details of these methods, so I would
like to first complete
-
order
- "A simple method to find out when an ordinary differential equation is
separable" by José ́Ángel Ci
- fixing problem with Lie groups and symmetry method.
- "Solving Differential Equations in Terms of Bessel Functions" by
Ruben Debeerst and Airy's function.
- Corresponding ISSAC 08 paper:
http://rubendebeerst.de/master/paper_issac2008.pdf and a pr.
<https://github.com/sympy/sympy/pull/10870>
On Sunday, March 17, 2019 at 7:54:59 PM UTC+5:30, rituraj singh wrote:
>
> Hello, Everyone
> Myself Ritu Raj Singh, sophomore of IIT BHU Varanasi.( GitHub profile
> <https://github.com/RituRajSingh878>)
>
> I would like to work on the implementation of ODE's solution this summer
> in my GSoC.
>
> Currently, SymPy only supports many basic types of differential equations,
> but there are plenty of methods that are not implemented.
>
>
> -
>
> Separation ansatz:
> - "A simple method to find out when an ordinary differential equation
> is separable" by José ́Ángel Cid( currently working on this
> <https://github.com/sympy/sympy/pull/16279> with the help of smichr
> <https://github.com/smichr> )
> -
>
> "Solving Differential Equations in Terms of Bessel Functions" by Ruben
> Debeerst.
> - Webpage: http://rubendebeerst.de/master/
> - Master Thesis: http://rubendebeerst.de/master/master.pdf
> - Corresponding ISSAC 08 paper:
> http://rubendebeerst.de/master/paper_issac2008.pdf.
> <http://rubendebeerst.de/master/paper_issac2008.pdf>
> -
>
> Lie groups and symmetry-related:
> - An implementation of these methods was done for first order ODEs
> during gsoc13. But we can do the same tricks for second order ODEs too.
> - "Computer Algebra Solving of First Order ODEs Using Symmetry
> Methods" by E.S. Cheb-Terrab, L.G.S. Duarte and L.A.C.P. da Mota. There
> is
> a short (15 pages) and an updated (24 pages) version of this paper.
> - "Computer Algebra Solving of Second Order ODEs Using Symmetry
> Methods" by E.S. Cheb-Terrab, L.G.S. Duarte, L.A.C.P. da Mota
> - "Integrating factors for second order ODEs" by E.S. Cheb-Terrab
> and A.D. Roche
> - "Symmetries and First Order ODE Patterns" by E.S. Cheb-Terrab and
> A.D. Roche
> - "Abel ODEs: Equivalence and Integrable Classes" by E.S.
> Cheb-Terrab and A.D. Roche Note: Original version (12 pages): July
> 1999.
> Revised version (31 pages): January 2000
> - "First order ODEs, Symmetries, and Linear Transformations" by
> E.S. Cheb-Terrab and T. Kolokolnikov
> - "Non-Liouvillian solutions for second order linear ODEs" by L.
> Chan, E.S. Cheb-Terrab.
>
> So I would like to work to complete these tasks.
>
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