PDE Solver Calculator

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Frequently asked

Yes. Click the green 📷 Scan button next to the mode chips, upload a photo or PDF, and our AI extracts the PDE type (heat, wave, Laplace, etc.), parameters, initial conditions, and boundary conditions.
A PDE involves a function of several variables and its partial derivatives. Three classic types: heat (diffusion), wave (propagation), Laplace (steady-state).
Dirichlet fixes the value u = g on the boundary (e.g. temperature held at the rod ends). Neumann fixes the derivative du/dn = g (insulated ends, no flux). Robin combines both (a·u + b·du/dn = g) for convective heat transfer. Dropdown labels in this calculator include the physical interpretation alongside the mathematical name.
The CFL condition ensures stability in finite difference methods. For heat: r = k·Δt/Δx² ≤ 0.5. For wave: C = c·Δt/Δx ≤ 1. Violating these blows up the numerical solution.
Assume u(x,t) = X(x)·T(t). Substituting separates the PDE into independent ODEs. Combined with boundary conditions, this yields eigenvalues / eigenfunctions and a Fourier series solution.
∂u/∂t = k∂²u/∂x² models heat diffusion, chemical concentration spread, and Black-Scholes option pricing. Parabolic.
∂²u/∂t² = c²∂²u/∂x² models vibrating strings, sound waves, electromagnetic radiation, and seismic waves. D'Alembert: u(x,t) = f(x-ct) + g(x+ct). Hyperbolic.
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Yes — over 2,000 PDE practice problems. Filter by 48 question types and 4 difficulty levels.
48 problem types: classification (basic), separation of variables and Fourier coefficients (medium), full Fourier series (hard), and Sturm-Liouville eigenvalue problems / Green's functions / biharmonic equations (scholar).