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PDE LaboratoryAll functions are free

PDE Laboratory

Compare the evolution of heat conduction, fluctuations, reaction diffusion, and viscous flow.

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Periodic boundary one-dimensional heat equation, wave equation, viscous Burgers equation; two-dimensional Gray–Scott reaction diffusion. Fixed grid, showing discrete methods and limitations.

PDE Laboratory: uses and methods

Compare the evolution of heat conduction, fluctuations, reaction diffusion, and viscous flow.

Applicable scope and calculation boundary

Periodic boundary one-dimensional heat equation, wave equation, viscous Burgers equation; two-dimensional Gray–Scott reaction diffusion. Fixed grid, showing discrete methods and limitations.

model and reference method

FFT spectral solution/spectral derivative; method line integration; explicit difference.

model version: 1.0.0. The results are used for scientific research, exploration and teaching, please interpret according to the model conditions.

input parameters

equation
One-dimensional heat equation / One-dimensional wave equation / One-dimensional sticky Burgers / two-dimensional reaction diffusion
Diffusion rate / wave speed
Value range: 0.005 – 2
evolution time
Value range: 0.05 – 10

How to use

  1. Load the example or enter data that matches the field description.
  2. Confirm units and models, run calculations and check diagnostics.
  3. Export charts, tables or results packages and record model versions.

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commercial application case

Industry Application · Independent Reproduction Example

Numerical prototype of thermal diffusion and fluctuation

R&D team first used regular grids to check the influence of diffusion parameters and boundary conditions. The

Public industry reference: COMSOL Multiphysics

COMSOL provides multiphysics modeling based on partial differential equations.

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  1. selection equation
  2. Set boundaries and grids
  3. Observation field evolution

Deliverables

Simplified field visualization for numerical methods and magnitude checks

needs to be checked before landing

does not contain arbitrary geometric meshes and engineering calibrations and is not a replacement for a complete multiphysics solution。

case is compiled for public industry purposes, and the reproduction steps are independent examples of this site; it does not mean that the above-mentioned institutions use or endorse this site, nor does it cite customer benefits that have not been publicly verified. The

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Mathematics

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  1. 01

    MIT · Department of Mathematics

    United States The

    Applied Mathematics, Dynamic Systems, Geometry and Numerical Analysis。

    official website link accessibility check: 2026-10-03
  2. 02

    University of Oxford · Mathematical Institute

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  3. 03

    Inria

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    Scientific Computing, Numerical Simulation and Computational Mathematics。

    official website entrance; please refer to the current public page of the institution.

catalog compiled on 2026-10-03. Link accessibility does not equate to verification of the latest papers, admissions, or program status; please check the institution's official website for specific research teams and opportunities.

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