◆ frontier30 mindraft

Solving in frequency space

Stop approximating derivatives locally. Represent the whole solution in a Fourier basis, where differentiation is multiplication and accuracy is exponential.

assumes you already have

Differentiating a function you can only sample

Planned outline

Differentiation as multiplication by ik in Fourier space.
Spectral accuracy: error falling faster than any power of h for smooth periodic functions.
Why one discontinuity destroys it - the Gibbs phenomenon.
Chebyshev bases for non-periodic domains.
Split-step and pseudo-spectral methods for nonlinear PDEs.
The cost: global coupling, FFT-shaped grids, hard boundary conditions.

Interactives planned

Each numbered point above gets at least one thing you can manipulate, not a figure. See AGENTS.md for the widget vocabulary and the rule that every lesson ships at least one graded interaction and one recall card.