Numerical solve the ordinary differential equation with python

Some excellent instructions are listed below.

It is real very easy to get it.

https://physics.nyu.edu/pine/pymanual/html/chap9/chap9_scipy.html

https://sam-dolan.staff.shef.ac.uk/mas212/notebooks/ODE_Example.html

https://scipy.github.io/old-wiki/pages/Cookbook/CoupledSpringMassSystem.html

https://apmonitor.com/pdc/index.php/Main/SolveDifferentialEquations

https://scicomp.stackexchange.com/questions/34304/solving-coupled-differential-equations-in-python-2nd-order

https://pundit.pratt.duke.edu/wiki/Python:Ordinary_Differential_Equations

https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_bvp.html?highlight=s

https://stackoverflow.com/questions/51733696/specify-different-timepoints-for-boundary-conditions-of-scipys-odeint/51734783#51734783

https://stackoverflow.com/questions/59379143/how-to-solve-a-simple-boundary-value-problem-for-tise-on-python

https://pav.iki.fi/software/bvp/index.html

https://pythonhosted.org/scikits.bvp_solver/tutorial.html

https://simlab.usask.ca/?page_id=580  #py_bvp

 Just do it!

https://documents.uow.edu.au/~buyung/EngineeringComputingLecture.pdf

http://www.ohiouniversityfaculty.com/youngt/IntNumMeth/lecture34.pdf

https://www.mathstat.dal.ca/~iron/math3210/bvp.pdf

http://folk.ntnu.no/leifh/teaching/tkt4140/._main044.html

http://web.cs.iastate.edu/~cs577/handouts/ode-boundary-value.pdf

http://fracton.khu.ac.kr/~syook/Lectures/ComputPhys/Newman/chap8.pdf

https://en.wikipedia.org/wiki/Jacobi_method

multiple shooting

A First Course in Ordinary Differential Equations (book)

newton method

https://www.lakeheadu.ca/sites/default/files/uploads/77/docs/RemaniFinal.pdf

equal to http://folk.ntnu.no/leifh/teaching/tkt4140/._main046.html

henyey relaxation

http://faculty.etsu.edu/lutter/courses/phys4007/p4007chap08.pdf

Finite Difference Schemes from 1st to 4th order

https://www.mech.kth.se/~ardeshir/courses/literature/fd.pdf

https://www.mathematik.uni-dortmund.de/~kuzmin/cfdintro/lecture4.pdf

Implicit Euler method

http://www.maths.lth.se/na/courses/FMN081/FMN081-06/lecture22.pdf#page=6

http://homepage.math.uiowa.edu/~whan/3800.d/S8-4.pdf

http://www.maths.lth.se/na/courses/FMN130/media/material/Chapter2.08a.pdf

SUite of Nonlinear and DIfferential/ALgebraic Equation Solvers

https://computing.llnl.gov/projects/sundials

Solving differential equations using modified Picard iteration

https://www.tandfonline.com/doi/abs/10.1080/00207391003675182

sympy

https://www.sympy.org/scipy-2017-codegen-tutorial/notebooks/20-ordinary-differential-equations.html