API Reference#

This page provides an overview of the spectral package API.

Spectral Basis Classes#

Classes for spectral methods on different bases.

`LegendreLobattoBasis`	Legendre-Gauss-Lobatto nodal polynomial basis.
`FourierEquispacedBasis`	Equispaced Fourier basis on a periodic interval.

Functions to construct differentiation and mass matrices.

`legendre_diff_matrix`	Return Legendre spectral differentiation matrix at arbitrary nodes.
`legendre_mass_matrix`	Return Legendre spectral mass matrix using normalized basis.
`fourier_diff_matrix_cotangent`	Construct Fourier differentiation matrix using cotangent identity.
`fourier_diff_matrix_on_interval`	Fourier differentiation matrix rescaled to periodic interval \([a, b]\).

Solvers for boundary value problems (BVPs).

`BvpProblem`	Dense linear BVP system with convenience helpers.
`solve_bvp`	Solve Exercise B: Laplace's equation in polar coordinates using mixed spectral collocation.
`solve_legendre_collocation`	Solve Exercise A boundary value problem using Legendre-Gauss-Lobatto collocation.
`solve_legendre_tau`	Solve Exercise A boundary value problem using Legendre tau method.
`solve_polar_bvp`	Solve Exercise B: Laplace's equation in polar coordinates using mixed spectral collocation.

Time integrators and PDE solvers.

`TimeIntegrator`	Base class for time integration methods.
`get_time_integrator`	Retrieve a time integrator by name.
`RK3`	3rd-order Strong Stability Preserving Runge-Kutta (SSP-RK3).
`RK4`	Classical 4th-order Runge-Kutta method (ERK4).

`KdVSolver`	Korteweg-de Vries equation solver using Fourier spectral methods.
`soliton`	Compute KdV soliton solution.
`two_soliton_initial`	Initial condition for two-soliton collision simulation.

Helper functions for I/O, formatting, plotting, and numerical analysis.

`io.ensure_output_dir`	Ensure output directory exists, creating it if necessary.
`io.load_simulation_data`	Load simulation data with automatic fallback between parquet and pickle.
`io.save_simulation_data`	Save simulation data to disk.
`formatting.extract_metadata`	Extract metadata from a DataFrame.
`formatting.format_dt_latex`	Format a timestep value as LaTeX scientific notation.
`formatting.format_parameter_range`	Format a parameter range for display.
`formatting.build_parameter_string`	Build a parameter string from a dictionary.
`plotting.get_repo_root`	Get repository root directory, handling both local and sphinx-gallery execution.
`norms.discrete_l2_norm`	Approximate L2 norm using composite trapezoidal rule.
`norms.discrete_l2_error`	Compute discrete L2 error between exact and numerical solutions.
`norms.discrete_linf_error`	Compute discrete \(L^\infty\) (maximum) error.