Module heat 

Heat equation solver

Solves the heat equation: ∂u/∂t = α∇²u

⚠️ CURRENT LIMITATION: Returns solutions with symbolic Fourier coefficients (A₁, A₂, A₃, …). Numerical evaluation of these coefficients requires symbolic integration, which is not yet implemented in MathHook.

What you get: Correct solution structure u(x,t) = Σ Aₙ sin(√λₙ x) exp(-λₙ α t) where λₙ are correctly computed eigenvalues

What’s missing: Actual values of Aₙ computed from initial conditions via Fourier series expansion (requires symbolic integration)

Examples

// This returns a solution with correctly computed eigenvalues
// but symbolic coefficients A_1, A_2, A_3, ...
let solution = solver.solve_heat_equation_1d(&pde, &alpha, &[bc1, bc2], &ic);
// solution.eigenvalues = [(π)², (2π)², (3π)², ...]  (correctly computed)
// solution.coefficients = [A_1, A_2, A_3, ...]  (symbolic, not computed)

Uses separation of variables and Fourier series for standard boundary conditions.

Structs

HeatEquationSolver

Heat equation solver implementing PDESolver trait

HeatSolutionDeprecated

Solution to the heat equation (legacy type for backward compatibility)

Functions

solve_heat_equation_1dDeprecated