Expand description
Heat equation solver
Solves the heat equation: du/dt = alpha * nabla^2(u)
Uses separation of variables and Fourier series for standard boundary conditions.
§Limitations
Returns solutions with symbolic Fourier coefficients (A_1, A_2, A_3, …). Numerical evaluation of these coefficients requires symbolic integration, which is not yet implemented in MathHook.
What you get: Correct solution structure u(x,t) = sum A_n sin(sqrt(lambda_n) x) exp(-lambda_n alpha t)
where lambda_n are correctly computed eigenvalues.
What’s missing: Actual values of A_n computed from initial conditions via Fourier series expansion (requires symbolic integration).
Structs§
- Heat
Equation Solver - Heat equation solver implementing PDESolver trait