PDE Solver
Use one numerical workbench to switch among several canonical partial differential equations. Select a grid, time step and physical coefficients, then inspect stability metrics, time snapshots or the converged two-dimensional field.
How this tool works
Spatial derivatives are discretized with finite differences. Time-dependent problems use explicit FTCS, leapfrog/upwind or Crank–Nicolson depending on the selected PDE; elliptic problems solve the resulting finite-difference linear system or iterate to steady state.
Example
Start with the heat equation using sin(πx), then switch to Crank–Nicolson without changing the physical diffusivity. Compare the stability warning and the final temperature profile.
Common questions
Can I type an arbitrary PDE?
Not on this page. The workbench focuses on canonical equations with well-defined discretizations so the result and stability metric remain transparent.
What boundary conditions are used?
The one-dimensional heat, wave, Poisson and reaction–diffusion examples use fixed zero endpoints; advection uses a periodic grid; the 2-D Laplace example uses a unit top boundary with zero on the other three sides.