# Solving the diffusion equation in Julia

**URL:** <https://discourse.julialang.org/t/solving-the-diffusion-equation-in-julia/28811>\
**Category:** Performance\
**Created:** [September 16, 2019, 2:25pm UTC](https://discourse.julialang.org/t/solving-the-diffusion-equation-in-julia/28811 "2019-09-16T14:25:35Z")\
**Posts on this page:** 4\
**Page:** 2

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**Author:** ![jtgreen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jtgreen/32/44908_2.png) [@jtgreen](https://discourse.julialang.org/u/jtgreen)\
**Post date:** [December 21, 2022, 4:52pm UTC](https://discourse.julialang.org/t/solving-the-diffusion-equation-in-julia/28811/21 "2022-12-21T16:52:28Z")

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Happy to, but in what form do you need? As I’m sure you know, most of these cardiac cell models are described as a set of ODE’s then kind of upgraded to a PDE by adding the diffusion term a la a cable equation/reaction diffusion system.

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**Author:** ![jtgreen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jtgreen/32/44908_2.png) [@jtgreen](https://discourse.julialang.org/u/jtgreen)\
**Post date:** [December 21, 2022, 4:52pm UTC](https://discourse.julialang.org/t/solving-the-diffusion-equation-in-julia/28811/22 "2022-12-21T16:52:59Z")

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per your request: ping.

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**Author:** ![xtalax](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/xtalax/32/35293_2.png) [@xtalax](https://discourse.julialang.org/u/xtalax)\
**Post date:** [December 21, 2022, 4:54pm UTC](https://discourse.julialang.org/t/solving-the-diffusion-equation-in-julia/28811/23 "2022-12-21T16:54:23Z")

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As a list of equations and boundary conditions along with the domain would work, best in PDE form or as close as you can manage, or a list of ODEs and PDEs

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [December 22, 2022, 10:53pm UTC](https://discourse.julialang.org/t/solving-the-diffusion-equation-in-julia/28811/24 "2022-12-22T22:53:59Z")

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> [@jtgreen](#):
>
> What in your opinion (taking this answer as a hint) is the simplest way to define and solve a reaction diffusion equation that is very large, stiff and solved on the GPU?

This is now addressed in the new SciML showcase.

> **[GPU-Accelerated Stochastic Partial Differential Equations · Overview of...](https://docs.sciml.ai/Overview/dev/showcase/gpu_spde/)**
>
> Documentation for Overview of Julia's SciML.

Once we fix the deployment issues, that will be the new stable version of the SciML overview documentation.

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