Implementation of ODE's solution.

[rituraj singh]

Hello, Everyone

Myself Ritu Raj Singh, sophomore of IIT BHU Varanasi.( GitHub profile)

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 with the help of 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.

• 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.

[Oscar Benjamin]

Great.

The separation ansatz and the Bessel function idea are both good. I
believe someone started a PR at some point for Bessel/Airy functions
so probably good to look at that as well.

For Lie groups the existing code needs substantial improvement. It is
largely untested and has many bugs. If that code was in an open PR now
then I would object to merging it. I think the priority there is not
so much extending the Lie group solvers but fixing what is already
there and coming up with good examples for tests that actually cover
the different branches of the code.

--
Oscar

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[rituraj singh]

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.

  
  

[rituraj singh]

I have listed these methods for this year of gSoc.I think all these are enough for a gSoc period -

• Separation ansatz:

  • "A simple method to find out when an ordinary differential equation is separable" by José ́Ángel Cid

• "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

• Lie groups and symmetry related:
  

  • Fixing bugs with Lie grouos and symmetry related and add test case.
    

• • "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

• • "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

[rituraj singh]

I have submitted my final application. Can you check it and give some suggestions -https://github.com/sympy/sympy/wiki/GSoC-2019-Current-Applications