Numerical Methods for Life123

[BrainAnnex]

UPDATE: this thread will be about GENERAL numerical methods; a separate thread will focus on "finite element methods" for solving the diffusion equation.

A definite source of complexity for Life123 are the complex boundary conditions. From early on - probably starting in a couple of Beta releases from now - an integral part of Life123 will be membranes and sub-cellular compartments... as well as the varying dimensions of the simulated cells.

Life123 will strive for a dual approach of helping non-experts feel more at ease, as well as trying to recruit contributors with deep expertise in the field.

The Diffusion page on the site has expanded a lot over time, and will take on an increasingly prominent role.

I've been reviewing the literature on numerical methods and PDEs (Partial Differential Equations): for the latter, see the separate thread

One 2022 ebook that I like is "Practical Numerical Computing Using Python", by Mahendra Verma (on Amazon)

It's pretty general, and covers tons of topics. It also lightly covers "Solving PDEs using Finite Difference Method" (chapter 16)

It pointed me to the Numpy Gradient method - which I wasn't aware of - to compute some of numerical differences that are used in Finite Difference Methods

[BrainAnnex]

A promising 2020 book that has come to my attention is "A Gentle Introduction To Numerical Simulations With Python", by S. Linge, H. P. Langtangen, 2nd edn
Chapter 9 is on solving PDEs... and, conveniently for our purposes, it focuses on the diffusion equation :)
On Amazon

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