Finite difference for BVP in Python

[Aber]

Hey poeops. I am trying to learn some nunerical math using the book Finite Difference Methods for Ordinary and Partial Differential Equations: Steady State and Time Dependent Problems by Randall J. LeVeque.

This post is regarding chapter 2 in the book. I want to run through an example in the book which is discussed here:

Non-linear Boundary Value Problem. How to compute the Jacobian?

Consider a Boundary Value Problem: $$ \delta u''+u(u'-1) =0 \Leftrightarrow u''=\frac{-u(u'-1)}{\delta}=:f(t,u',u), \\ u(0)=a, u(1)=b $$ $\delta,a,b$ are known parameters. I want to implement New...

scicomp.stackexchange.com

At the end of the first answer by VoB there is Octave code. Unfortunately I don't have that program. does anyone by any chance similar code in Python? Or can transle that in Python and numpy?

I know I might appear extremely lazy by not doing it myself but this will take me a whole day( I am not the best programmer), which is too long for "just" a demonstration of example

 

[Daniel Duffy]

Don't be lazy, be clever

solve_bvp — SciPy v1.14.0 Manual

docs.scipy.org

I reckon the Jacobian is taken care of in the solver? (default, J is done for you by fd).


God luck; let us know how you get on.

y'' + k * exp(y) = 0
y(0) = y(1) = 0

for k = 1.