PDE Lab (Finite Differences) — Heat, Wave, Laplace | GetCalcMaster
Discretize and simulate classic PDEs using finite differences. Explore stability, boundary conditions, and grid refinement — then export to the notebook.
PDE Lab (Finite Differences)
The PDE Lab helps you experiment with partial differential equations using finite difference discretizations. It’s built to make the grid, time step, and boundary conditions explicit so you can reason about stability and accuracy.
What you can do
- Set up classic PDEs (heat/wave/Laplace-style patterns) with boundary conditions.
- Run time stepping and visualize behavior on a grid.
- Refine grid/time step to test convergence.
Stability and refinement
Finite difference schemes can be stable or unstable depending on parameters (e.g., time step relative to grid spacing). A good practice is to:
- run a refinement sweep (smaller grid spacing / time step),
- check whether the qualitative solution and key metrics converge,
- document boundary conditions and discretization choices in the notebook.
FAQ
What are boundary conditions and why do they matter?
Boundary conditions specify behavior on the domain boundary (fixed values, derivatives, periodicity). They can completely change the PDE solution, so they must be stated clearly.
How do I check if my PDE simulation is reliable?
Refine the grid and time step and look for stable results. If solutions change dramatically under refinement, your discretization or parameters may be unstable.
Can I use this for research-grade PDE solving?
The lab is designed for learning and verification workflows. For high-stakes PDE simulation, validate with dedicated numerical libraries and established benchmarks.