⚡ Interactive Tool

Partial Differential Equation Solver

Solve and visualize fundamental PDEs using finite difference methods. Select an equation, configure parameters, and watch the solution evolve in real time.

⚙️ Configuration

0.25
0.5
Dirichlet
Neumann
Periodic
Robin
Ready
∂u/∂t = α ∇²u

Configure your PDE and click "Solve Equation"

Results will appear here in real time
Time Step t = 0

📊 Solution Info

📐 Selected Equation

∂u/∂t = α ∂²u/∂x²
1D Heat Equation
The heat equation models heat diffusion. Solved here using the FTCS (Forward-Time Central-Space) finite difference scheme with explicit time stepping.

📊 Numerical Stats

Grid Resolution 80 pts
CFL Number
Time Step (Δt)
Spatial Step (Δx)
Compute Time
Status Not run

📈 Convergence

Progress 0%

🖥️ Solver Console

[--:--:--] Aevum PDE Solver initialized. Select an equation and click Solve.
🔥

Heat Equation

Models how temperature diffuses through a medium over time. The solution smooths out initial temperature variations, governed by the material's thermal diffusivity coefficient α.

🌊

Wave Equation

Describes wave propagation in strings, membranes, and acoustic fields. Solutions represent traveling waves that preserve shape while propagating at speed c through the medium.

⚖️

Laplace Equation

Governs steady-state phenomena: electrostatic potentials, incompressible fluid flow, and gravitational fields. Solutions are harmonic functions with no local extrema in the interior.

💨

Advection Equation

Models transport of a quantity by a flow field. The solution represents a waveform that translates without changing shape at the velocity v of the underlying flow.