# \#pde

**URL:** https://discourse.julialang.org/tag/pde/174.md

[Latest](https://discourse.julialang.org/latest.md) · [Categories](https://discourse.julialang.org/categories.md) · [Tags](https://discourse.julialang.org/tags.md)

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## [\[ANN\] ReactionDiffusion.jl v1.0.0 - Simulation and visualization for 1D reaction-diffusion systems](https://discourse.julialang.org/t/ann-reactiondiffusion-jl-v1-0-0-simulation-and-visualization-for-1d-reaction-diffusion-systems/139041)

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**Author:** [@homocarbonis](https://discourse.julialang.org/u/homocarbonis)\
**Replies:** 0\
**Last updated:** [August 25, 2026, 6:36pm UTC](https://discourse.julialang.org/t/ann-reactiondiffusion-jl-v1-0-0-simulation-and-visualization-for-1d-reaction-diffusion-systems/139041 "2026-08-25T18:36:45Z")

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I’d like to announce a brand new version of ReactionDiffusion.jl, a general purpose toolkit for anyone interested in modelling reaction-diffusion systems on a 1D domain. This release builds on the design of its predece…

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## [\[ANN\] LowLevelFEM.jl is now published in JOSS](https://discourse.julialang.org/t/ann-lowlevelfem-jl-is-now-published-in-joss/138524)

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**Author:** [@perebalazs](https://discourse.julialang.org/u/perebalazs)\
**Replies:** 0\
**Last updated:** [July 29, 2026, 9:43am UTC](https://discourse.julialang.org/t/ann-lowlevelfem-jl-is-now-published-in-joss/138524 "2026-07-29T09:43:01Z")

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I’m happy to share that LowLevelFEM.jl has been published in the Journal of Open Source Software (JOSS). LowLevelFEM.jl is a lightweight finite element toolbox written in Julia for education, research, and rapid prototy…

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## [Boundary Condition Error in MethodOfLines](https://discourse.julialang.org/t/boundary-condition-error-in-methodoflines/137819)

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**Author:** [@ducksoverip](https://discourse.julialang.org/u/ducksoverip)\
**Replies:** 2\
**Last updated:** [June 29, 2026, 12:53pm UTC](https://discourse.julialang.org/t/boundary-condition-error-in-methodoflines/137819 "2026-06-29T12:53:59Z")

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I’m trying to use MethodOfLines to solve the time-independent Schrodinger equation for hydrogen, as a prelude to more complicated systems. The equation is as follows: \\nabla^2 \\psi(\\vec{r}) - \\frac{1}{r}\\psi(\\vec{r}) =…

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## [Is there a general guide to Julia's PDE solving utilities based on the properties of the PDE in question?](https://discourse.julialang.org/t/is-there-a-general-guide-to-julias-pde-solving-utilities-based-on-the-properties-of-the-pde-in-question/137545)

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**Author:** [@ducksoverip](https://discourse.julialang.org/u/ducksoverip)\
**Replies:** 2\
**Last updated:** [June 10, 2026, 7:30pm UTC](https://discourse.julialang.org/t/is-there-a-general-guide-to-julias-pde-solving-utilities-based-on-the-properties-of-the-pde-in-question/137545 "2026-06-10T19:30:56Z")

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As I continue my foray into Julia, I’d like to apply it more directly to my research by utilizing its PDE-solving capabilities to solve the radial Schrodinger equation for one and two-electron systems, with an eye toward…

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## [Vibe-coded modelingtoolkit code generation for PDEs](https://discourse.julialang.org/t/vibe-coded-modelingtoolkit-code-generation-for-pdes/136701)

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**Author:** [@ctessum](https://discourse.julialang.org/u/ctessum)\
**Replies:** 0\
**Last updated:** [April 13, 2026, 4:55pm UTC](https://discourse.julialang.org/t/vibe-coded-modelingtoolkit-code-generation-for-pdes/136701 "2026-04-13T16:55:53Z")

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The current released version of ModelingToolkit.jl + MethodOfLines.jl doesn’t really work when the number of variables x the number of grid points is more than ~1,000. In case it is of interest, I’ve created some vibe-c…

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## [\[GSoC '26\] The Illusion of Uniformity: Non-Uniform Grids & Zero-Overhead Dispatch in MOL.jl](https://discourse.julialang.org/t/gsoc-26-the-illusion-of-uniformity-non-uniform-grids-zero-overhead-dispatch-in-mol-jl/136639)

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**Author:** [@Utku\_Yilmaz](https://discourse.julialang.org/u/Utku_Yilmaz)\
**Replies:** 0\
**Last updated:** [April 9, 2026, 10:00am UTC](https://discourse.julialang.org/t/gsoc-26-the-illusion-of-uniformity-non-uniform-grids-zero-overhead-dispatch-in-mol-jl/136639 "2026-04-09T10:00:18Z")

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Hi everyone, As part of my GSoC 2026 prep for MethodOfLines.jl, I just published a short devlog on bringing non-uniform grid support to high-order schemes like WENO. My post, “The Illusion of Uniformity,” outlines the a…

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## [\[ANN\] LowLevelFEM.jl – assembling PDE systems directly from weak forms](https://discourse.julialang.org/t/ann-lowlevelfem-jl-assembling-pde-systems-directly-from-weak-forms/136136)

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**Author:** [@perebalazs](https://discourse.julialang.org/u/perebalazs)\
**Replies:** 13\
**Last updated:** [March 13, 2026, 8:43pm UTC](https://discourse.julialang.org/t/ann-lowlevelfem-jl-assembling-pde-systems-directly-from-weak-forms/136136 "2026-03-13T20:43:23Z")

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I’ve been working on a small Julia FEM framework called LowLevelFEM.jl. One of the ideas behind the project is to assemble PDE systems directly from their weak form. The core idea is simple: If you know the weak form o…

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## [Minisymposium on Partial Differential Equations and its Applications (Juliacon 2026)](https://discourse.julialang.org/t/minisymposium-on-partial-differential-equations-and-its-applications-juliacon-2026/135600)

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**Author:** [@Arpit\_Babbar](https://discourse.julialang.org/u/Arpit_Babbar)\
**Replies:** 0\
**Last updated:** [February 12, 2026, 4:40pm UTC](https://discourse.julialang.org/t/minisymposium-on-partial-differential-equations-and-its-applications-juliacon-2026/135600 "2026-02-12T16:40:45Z")

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We are eager to receive talk contributions for our minisymposium on partial differential equations (PDE) at Juliacon 2026. The minisymposium will cover everything that relates to Julia and PDEs, including but not limited…

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## [Feedback wanted: GPU-accelerated 2D elastic wave simulation (staggered-grid FD) in Julia](https://discourse.julialang.org/t/feedback-wanted-gpu-accelerated-2d-elastic-wave-simulation-staggered-grid-fd-in-julia/134869)

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**Author:** [@Wuheng10086](https://discourse.julialang.org/u/Wuheng10086)\
**Replies:** 10\
**Last updated:** [January 10, 2026, 3:16pm UTC](https://discourse.julialang.org/t/feedback-wanted-gpu-accelerated-2d-elastic-wave-simulation-staggered-grid-fd-in-julia/134869 "2026-01-10T15:16:09Z")

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Hi everyone, I’m currently working on a GPU-accelerated 2D elastic wave simulation code in Julia, based on staggered-grid finite-difference discretization. The original motivation is seismic forward modeling, but I’m …

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## [Method Error when using Method of Lines to solve PDEs](https://discourse.julialang.org/t/method-error-when-using-method-of-lines-to-solve-pdes/132951)

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**Author:** [@gst1017](https://discourse.julialang.org/u/gst1017)\
**Replies:** 3\
**Last updated:** [October 24, 2025, 3:52pm UTC](https://discourse.julialang.org/t/method-error-when-using-method-of-lines-to-solve-pdes/132951 "2025-10-24T15:52:53Z")

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Hello all! I’m new to Julia and am trying to use the Method of Lines and MTK packages to solve a system of PDEs. I am running into repeated method errors, and the stacktrace keeps pointing to a line from Macro Expanded c…

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## [Interpolated parameters into the PDESystems](https://discourse.julialang.org/t/interpolated-parameters-into-the-pdesystems/132736)

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**Author:** [@sraghuram](https://discourse.julialang.org/u/sraghuram)\
**Replies:** 6\
**Last updated:** [October 22, 2025, 12:47pm UTC](https://discourse.julialang.org/t/interpolated-parameters-into-the-pdesystems/132736 "2025-10-22T12:47:42Z")

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Hey I am trying to solve a system of equations where my input parameters are altitude dependent values. These values should be supplied into system of equations after discretizing the equation. I have created an Interpol…

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## [Solving a non-linear P(I)DE - neural field equation](https://discourse.julialang.org/t/solving-a-non-linear-p-i-de-neural-field-equation/132678)

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**Author:** [@jucheval](https://discourse.julialang.org/u/jucheval)\
**Replies:** 3\
**Last updated:** [September 29, 2025, 8:53am UTC](https://discourse.julialang.org/t/solving-a-non-linear-p-i-de-neural-field-equation/132678 "2025-09-29T08:53:16Z")

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Hi everyone ! I am searching for some way to solve the following non linear P(I)DE, known as the neural field equation: \\frac{\\partial}{\\partial\_t} u(t,x) = -\\alpha u(t,x) + \\int w(y,x) f(u(t,y)) dy, for some scalar \\…

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## [Solving a non-linear P(I)DE - age-structured equation](https://discourse.julialang.org/t/solving-a-non-linear-p-i-de-age-structured-equation/132677)

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**Author:** [@jucheval](https://discourse.julialang.org/u/jucheval)\
**Replies:** 5\
**Last updated:** [September 29, 2025, 8:51am UTC](https://discourse.julialang.org/t/solving-a-non-linear-p-i-de-age-structured-equation/132677 "2025-09-29T08:51:02Z")

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Hi everyone ! I am searching for some way to solve the following non-linear P(I)DE, known as the refractory density equation or age-structured equation: \\begin{cases} \\frac{\\partial}{\\partial\_t} u(t,a) + \\frac{\\pa…

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## [Solving the Boltzmann transport equation using Trixi.jl](https://discourse.julialang.org/t/solving-the-boltzmann-transport-equation-using-trixi-jl/132509)

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**Author:** [@drandran12](https://discourse.julialang.org/u/drandran12)\
**Replies:** 4\
**Last updated:** [September 19, 2025, 12:35pm UTC](https://discourse.julialang.org/t/solving-the-boltzmann-transport-equation-using-trixi-jl/132509 "2025-09-19T12:35:58Z")

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I need to solve the two spatial dimensional Boltzmann transport equation of the form: \\left\[\\partial\_t+\\vec{k} \\cdot \\vec{\\nabla}\_x-\\vec{\\nabla}\_x V \\cdot \\vec{\\nabla}\_k\\right\] n(\\vec{x}, t, \\vec{k})=-4 \\Gamma\_a \\int \\…

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## [\`NeuralPDE.jl\`: How to impose Dirichlet boundary conditions as hard constraints?](https://discourse.julialang.org/t/neuralpde-jl-how-to-impose-dirichlet-boundary-conditions-as-hard-constraints/132007)

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**Author:** [@Sigmund](https://discourse.julialang.org/u/Sigmund)\
**Replies:** 1\
**Last updated:** [September 6, 2025, 10:24pm UTC](https://discourse.julialang.org/t/neuralpde-jl-how-to-impose-dirichlet-boundary-conditions-as-hard-constraints/132007 "2025-09-06T22:24:28Z")

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Im solving a coupled PDE-problem using NeuralPDE.jl, the boundary conditions are now set by the penalization method. Instead I want to apply these as hard boundary constraints, or as an output transformation, as it is d…

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## [How to discretize a PDE with a Moving Boundary? (a.k.a Stefan Problem, a.k.a Variable Boundary)](https://discourse.julialang.org/t/how-to-discretize-a-pde-with-a-moving-boundary-a-k-a-stefan-problem-a-k-a-variable-boundary/123687)

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**Author:** [@Jax\_Xu](https://discourse.julialang.org/u/Jax_Xu)\
**Replies:** 6\
**Last updated:** [August 26, 2025, 9:12am UTC](https://discourse.julialang.org/t/how-to-discretize-a-pde-with-a-moving-boundary-a-k-a-stefan-problem-a-k-a-variable-boundary/123687 "2025-08-26T09:12:30Z")

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Hi Community! I need your expertise :sob:! I am solving a 1D diffusion equation with a moving boundary. The physical background is the reaction of gas with a solid particle, where the gas diffuses through the product lay…

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## [Mean‐Field Games “Crowd Control” Problem in Julia: HJB OK, but Struggling With Fokker‐Planck Positivity in Gridap](https://discourse.julialang.org/t/mean-field-games-crowd-control-problem-in-julia-hjb-ok-but-struggling-with-fokker-planck-positivity-in-gridap/128134)

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**Author:** [@Ciccisio](https://discourse.julialang.org/u/Ciccisio)\
**Replies:** 2\
**Last updated:** [April 29, 2025, 10:21am UTC](https://discourse.julialang.org/t/mean-field-games-crowd-control-problem-in-julia-hjb-ok-but-struggling-with-fokker-planck-positivity-in-gridap/128134 "2025-04-29T10:21:30Z")

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Hi everyone, I’m relatively new to Julia and I’m trying to solve a crowd control Mean Field Game (MFG) problem (inspired by Yves Achdou’s work " Mean Field Games for Modeling Crowd Motion") consisting of: A Hamilton–J…

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## [How to solve partial differential algebraic equations](https://discourse.julialang.org/t/how-to-solve-partial-differential-algebraic-equations/113989)

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**Author:** [@Anish\_Kumar](https://discourse.julialang.org/u/Anish_Kumar)\
**Replies:** 8\
**Last updated:** [April 15, 2025, 8:09am UTC](https://discourse.julialang.org/t/how-to-solve-partial-differential-algebraic-equations/113989 "2025-04-15T08:09:10Z")

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Hi all, I am quite new to Julia and programming in general. I am currently doing a modelling PhD and I have a set of couple Partial Differential Algebraic Equations (PDAE). I tried solving them on comsol but it is extre…

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## [What is the best way to implement PINN in Julia](https://discourse.julialang.org/t/what-is-the-best-way-to-implement-pinn-in-julia/127713)

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**Author:** [@Yang-yang](https://discourse.julialang.org/u/Yang-yang)\
**Replies:** 18\
**Last updated:** [April 6, 2025, 2:37pm UTC](https://discourse.julialang.org/t/what-is-the-best-way-to-implement-pinn-in-julia/127713 "2025-04-06T14:37:28Z")

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Dear all, I want to use PINNs to solve a PDE. There are two packages in Julia that can do this NeuralPDE.jl and Sophon.jl Both of these packages use the finite difference method to realize derivatives. I want to know i…

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## [Solution not converging for advection PDE](https://discourse.julialang.org/t/solution-not-converging-for-advection-pde/123349)

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**Author:** [@Alma\_Thindberg](https://discourse.julialang.org/u/Alma_Thindberg)\
**Replies:** 9\
**Last updated:** [March 25, 2025, 1:05pm UTC](https://discourse.julialang.org/t/solution-not-converging-for-advection-pde/123349 "2025-03-25T13:05:01Z")

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using Pkg #Pkg.add("ModelingToolkit") #Pkg.add("MethodOfLines") #Pkg.add("DomainSets") #Pkg.add("OrdinaryDiffEq") Pkg.add("NonlinearSolve") using ModelingToolkit, MethodOfLines, DomainSets, OrdinaryDiffEq, LinearAlge…

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## [PDE system solver](https://discourse.julialang.org/t/pde-system-solver/127046)

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**Author:** [@Anish\_Kumar](https://discourse.julialang.org/u/Anish_Kumar)\
**Replies:** 0\
**Last updated:** [March 17, 2025, 9:46am UTC](https://discourse.julialang.org/t/pde-system-solver/127046 "2025-03-17T09:46:48Z")

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Hi all, I am trying to solve

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## [Solving 2D PDE similar to advection-diffusion on unstructured mesh with Trixi](https://discourse.julialang.org/t/solving-2d-pde-similar-to-advection-diffusion-on-unstructured-mesh-with-trixi/125462)

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**Author:** [@Liris](https://discourse.julialang.org/u/Liris)\
**Replies:** 6\
**Last updated:** [February 5, 2025, 5:41pm UTC](https://discourse.julialang.org/t/solving-2d-pde-similar-to-advection-diffusion-on-unstructured-mesh-with-trixi/125462 "2025-02-05T17:41:52Z")

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Dear all, I am trying to solve the following equation: \\frac{\\partial \\phi}{\\partial t} + \\nabla\\cdot(\\phi \\boldsymbol{u}) - \\frac{\\partial}{\\partial z} \\left\[\\mathcal{F} \\phi(1-\\phi)\\right\] = \\nabla \\cdot (\\mathcal{D}…

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## [Order for finite elements when using Gridap and Gmsh](https://discourse.julialang.org/t/order-for-finite-elements-when-using-gridap-and-gmsh/125094)

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**Author:** [@mikeliux](https://discourse.julialang.org/u/mikeliux)\
**Replies:** 9\
**Last updated:** [January 27, 2025, 8:22am UTC](https://discourse.julialang.org/t/order-for-finite-elements-when-using-gridap-and-gmsh/125094 "2025-01-27T08:22:18Z")

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I am experimenting with Gridap package for solving partial differential equations (PDEs) in Julia. I am creating my meshes with GMSH, using the API provided by the Gmsh package in Julia. I save them as \*.msh files, and t…

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## [Compute integral for DelaunayTriangulation.jl to be able to solve PDE with FiniteVolumeMethod.jl](https://discourse.julialang.org/t/compute-integral-for-delaunaytriangulation-jl-to-be-able-to-solve-pde-with-finitevolumemethod-jl/124310)

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**Author:** [@B4rtel](https://discourse.julialang.org/u/B4rtel)\
**Replies:** 4\
**Last updated:** [January 2, 2025, 3:20pm UTC](https://discourse.julialang.org/t/compute-integral-for-delaunaytriangulation-jl-to-be-able-to-solve-pde-with-finitevolumemethod-jl/124310 "2025-01-02T15:20:13Z")

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Hi :), I would like to solve a advection PDE of the form \\frac{\\partial}{\\partial t} f(x,t) = - \\nabla\_x \\cdot \\left(\\left(\\int \[\\phi(p\_1(x,y),\\phi(p\_2(x,y)\]\\odot (y-x) f(y,t) \\text{d} y\\right) f(x,t)\\right) for p\_a(x\_i…

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## [Scaling issue (probably) while solving simple PINN problem](https://discourse.julialang.org/t/scaling-issue-probably-while-solving-simple-pinn-problem/124183)

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**Author:** [@nico](https://discourse.julialang.org/u/nico)\
**Replies:** 3\
**Last updated:** [December 27, 2024, 4:04pm UTC](https://discourse.julialang.org/t/scaling-issue-probably-while-solving-simple-pinn-problem/124183 "2024-12-27T16:04:14Z")

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Hi All! I am trying to solve a simple ODE with the PINN technology. There might be better ways to do that, but I am using it to test and understand few practical things. This code worked perfectly as long as the probl…

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## [Integrate convolution symbolically to solve PDE](https://discourse.julialang.org/t/integrate-convolution-symbolically-to-solve-pde/123810)

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**Author:** [@B4rtel](https://discourse.julialang.org/u/B4rtel)\
**Replies:** 2\
**Last updated:** [December 13, 2024, 9:32pm UTC](https://discourse.julialang.org/t/integrate-convolution-symbolically-to-solve-pde/123810 "2024-12-13T21:32:41Z")

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I would like to solve a PDE with MethodOfLines.jl and ModellingToolkit.jl similar to the example docs.sciml.ai/MethodOfLines/stable/tutorials/PIDE/. My modification is to change the integral term. Instead of integrating …

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## [NeuralPDE with tuple input](https://discourse.julialang.org/t/neuralpde-with-tuple-input/123078)

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**Author:** [@Yang-yang](https://discourse.julialang.org/u/Yang-yang)\
**Replies:** 4\
**Last updated:** [December 1, 2024, 1:20pm UTC](https://discourse.julialang.org/t/neuralpde-with-tuple-input/123078 "2024-12-01T13:20:23Z")

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I want to use the PINN to solve a PDE whose time dependence is mild, but its spatial dependence is complicated. I construct the following neural network, inner = 8 chain = Chain(Parallel(vcat, Chain(NoOpLayer())…

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## [Julia can be dramatically slower than Matlab when solving 2D PDE](https://discourse.julialang.org/t/julia-can-be-dramatically-slower-than-matlab-when-solving-2d-pde/122321)

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**Author:** [@Alex90](https://discourse.julialang.org/u/Alex90)\
**Replies:** 42\
**Last updated:** [November 9, 2024, 2:25pm UTC](https://discourse.julialang.org/t/julia-can-be-dramatically-slower-than-matlab-when-solving-2d-pde/122321 "2024-11-09T14:25:33Z")

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Hello, It is said that Julia is very fast in comparison with other high level languages. SInce i do scientific computing, i was interested in this language. So i compared performance of Julia and Matlab when solving two…

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## [NeuralPDE.jl slow with integro diff. equations](https://discourse.julialang.org/t/neuralpde-jl-slow-with-integro-diff-equations/122511)

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**Author:** [@nico](https://discourse.julialang.org/u/nico)\
**Replies:** 3\
**Last updated:** [November 11, 2024, 8:42pm UTC](https://discourse.julialang.org/t/neuralpde-jl-slow-with-integro-diff-equations/122511 "2024-11-11T20:42:40Z")

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Is there a reason why with integro-differential equations NeuralPDE.jl becomes very slow? Is there a better way to deal with integrals than with, e.g., Ii = Symbolics.Integral(t in DomainSets.ClosedInterval(0, t)) ?

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## [Did i coded my pde correctly?](https://discourse.julialang.org/t/did-i-coded-my-pde-correctly/121661)

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**Author:** [@Shashi2\_Kumar](https://discourse.julialang.org/u/Shashi2_Kumar)\
**Replies:** 0\
**Last updated:** [October 23, 2024, 5:08pm UTC](https://discourse.julialang.org/t/did-i-coded-my-pde-correctly/121661 "2024-10-23T17:08:55Z")

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After many weeks of search for a pde solver for my elliptic pde i came across Julia. Found that it has a FNC package (FundamentalsNumericalComputation) that solves pde. I tried to encode my pde with boundary conditions a…

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