Module separation_of_variables 

Separation of variables method for PDEs

This module implements complete separation of variables including:

• Eigenvalue problem solving with boundary conditions
• Fourier coefficient computation from initial conditions
• Complete series solution assembly

Implementation

For standard PDEs like heat and wave equations:

1. Assume product solution: u(x,t) = X(x)T(t)
2. Apply boundary conditions → solve eigenvalue problem for X(x)
3. Solve temporal ODE for T(t)
4. Apply initial conditions → compute Fourier coefficients
5. Assemble infinite series solution

Structs

SeparatedSolution

Result of applying separation of variables

Functions

construct_series_solution

Construct complete series solution from eigenvalues and coefficients

separate_variables

Applies separation of variables to a PDE with boundary and initial conditions