# 2d finite differences implementation for a Numerical Analysis lecture
**URL:** https://discourse.julialang.org/t/2d-finite-differences-implementation-for-a-numerical-analysis-lecture/70222
**Category:** Performance
**Tags:** numerics, finitediff
**Created:** [October 22, 2021, 3:32pm UTC](https://discourse.julialang.org/t/2d-finite-differences-implementation-for-a-numerical-analysis-lecture/70222 "2021-10-22T15:32:21Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@vicdolean](https://discourse.julialang.org/u/vicdolean)
#### Post date: [October 22, 2021, 3:32pm UTC](https://discourse.julialang.org/t/2d-finite-differences-implementation-for-a-numerical-analysis-lecture/70222/1 "2021-10-22T15:32:21Z")
Hi! I’m new to Julia world and would need some help in the transition from Matlab.
I am teaching a numerical analysis class where I use finite differences on a two dimensional (cartesian but not necessarily square) domain. The Matlab function **delsq** was very useful as I could then generate the grid by meshgrid, build the FD matrix from it, change boundary conditions to Neumann or Robin to a part of the boundary and also localise the source term, diffusion coeff etc…
I all want are simple teaching codes where I can illustrate all the basic concepts on finite differences in a genuinely 2d implementation (no kronecker of 1d!) - and not black box like in [[https://github.com/SciML/DifferentialEquations.jl](https://github.com/SciML/DifferentialEquations.jl)]
Has someone already tried that?
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### Author:  [@mauro3](https://discourse.julialang.org/u/mauro3)
#### Post date: [October 23, 2021, 7:58am UTC](https://discourse.julialang.org/t/2d-finite-differences-implementation-for-a-numerical-analysis-lecture/70222/2 "2021-10-23T07:58:15Z")
Maybe the codes in [https://github.com/luraess/parallel-gpu-workshop-JuliaCon21/tree/main/scripts](https://github.com/luraess/parallel-gpu-workshop-JuliaCon21/tree/main/scripts) can be of use, e.g. here diffusion with a forward euler step [https://github.com/luraess/parallel-gpu-workshop-JuliaCon21/blob/main/scripts/diffusion\_2D\_expl.jl](https://github.com/luraess/parallel-gpu-workshop-JuliaCon21/blob/main/scripts/diffusion_2D_expl.jl).
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### Author:  [@vicdolean](https://discourse.julialang.org/u/vicdolean)
#### Post date: [November 20, 2021, 8:43am UTC](https://discourse.julialang.org/t/2d-finite-differences-implementation-for-a-numerical-analysis-lecture/70222/3 "2021-11-20T08:43:03Z")
Thanks a lot! This is very useful.
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### Author:  [@pxshen](https://discourse.julialang.org/u/pxshen)
#### Post date: [June 22, 2022, 11:17pm UTC](https://discourse.julialang.org/t/2d-finite-differences-implementation-for-a-numerical-analysis-lecture/70222/4 "2022-06-22T23:17:38Z")
Check out this `EquivariantOperators.jl` [tutorial](https://colab.research.google.com/drive/17JZEdK6aALxvn0JPBJEHGeK2nO1hPnhQ#scrollTo=2xW0gUV_DFXT&line=1&uniqifier=1) and [package website](https://aced-differentiate.github.io/EquivariantOperators.jl/)
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### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [June 23, 2022, 12:22am UTC](https://discourse.julialang.org/t/2d-finite-differences-implementation-for-a-numerical-analysis-lecture/70222/5 "2022-06-23T00:22:31Z")
> [@vicdolean](#):
>
> I all want are simple teaching codes where I can illustrate all the basic concepts on finite differences in a genuinely 2d implementation (no kronecker of 1d!)
See, for example, [this post](https://discourse.julialang.org/t/seemingly-unnecessary-allocation-within-for-loop/72556/8), which provides a simple N-dimensional implementation of a finite-difference method for a wave equation using a leapfrog explicit timestepping scheme. It would be pretty easy to change it to the diffusion equation, too.
Among other things, it illustrates computing the finite-difference Laplacian in N dimensions cleanly and efficiently using Julia’s Cartesian-indexing code, and the useful technique of “ghost cells” for boundary conditions (which allow you to separate the boundary-condition code from the finite-difference code).
(Whoops, sorry, I see that this is an old thread that was recently revived.)