Module laplace 

Laplace equation solver

Solves the Laplace equation: ∇²u = 0

⚠️ CURRENT LIMITATION: Returns solutions with symbolic Fourier coefficients (C₁, C₂, C₃, …). Numerical evaluation of these coefficients requires symbolic integration, which is not yet implemented in MathHook.

What you get: Correct solution structure u(x,y) = Σ Cₙ sin(λₙx) sinh(λₙy) where λₙ = nπ/a are correctly computed eigenvalues

What’s missing: Actual values of Cₙ computed from boundary conditions

Examples

// This returns a solution with correctly computed eigenvalues
// but symbolic coefficients C_1, C_2, C_3, ...
let solution = solver.solve_laplace_equation_2d(&pde, &[bc1, bc2]);
// solution.x_eigenvalues = [π, 2π, 3π, ...]  (correctly computed)
// solution.coefficients = [C_1, C_2, C_3, ...]  (symbolic, not computed)

Structs

LaplaceEquationSolver

Laplace equation solver implementing PDESolver trait

LaplaceSolution

Solution to the Laplace equation

Functions

solve_laplace_2d

Legacy function for backward compatibility