# Stability of steady-state heat equation example for MethodOfLines.jl

**URL:** <https://discourse.julialang.org/t/stability-of-steady-state-heat-equation-example-for-methodoflines-jl/98651>\
**Category:** Modelling & Simulations\
**Tags:** pde\
**Created:** [May 10, 2023, 11:25pm UTC](https://discourse.julialang.org/t/stability-of-steady-state-heat-equation-example-for-methodoflines-jl/98651 "2023-05-10T23:25:44Z")\
**Posts on this page:** 1\
**Showing post:** 8

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**Author:** ![Eben60](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/eben60/32/13475_2.png) [@Eben60](https://discourse.julialang.org/u/Eben60)\
**Post date:** [August 31, 2024, 4:03pm UTC](https://discourse.julialang.org/t/stability-of-steady-state-heat-equation-example-for-methodoflines-jl/98651/8 "2024-08-31T16:03:46Z")

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Just stumbled upon the problem ☹  
Step of 0.1 works fine, step 0.05 diverges and stops on MaxIters, and step 0.025 or less appears to hang Julia, which doesn’t then react to Ctrl-C.

Are there any workarounds known (using some other algorithm instead of `NewtonRaphson` ??).

Alternative question: If I have a relatively simple 2D stationary diffusion problem, what is currently the way to go?

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