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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