What is PDE Solver 1D Heat Equation Calculator and Why it Matters?
The 1D heat equation models temperature diffusion. Explicit finite differences provide an accessible introduction to numerical PDEs.
Mathematical Formula and Theory
u_t = α u_xx. Explicit scheme: u_i^{n+1} = u_i^n + r(u_{i+1}^n − 2u_i^n + u_{i−1}^n), r=αΔt/Δx² ≤ 1/2 for stability.
How to Use This Calculator - Step by Step
- Set length, diffusivity, grid sizes, and final time.
- Click Solve Heat Equation.
Solved Example with Full Calculation
L=1, α=0.01, initial sin(πx). Center value decays consistently with the exact fundamental mode e^{−απ²T}.