A new method for fast transforms in parity-mixed PDEs: Part I. Numerical techniques and analysis

We address the problem of parity mixing, where the projection of a variable expressed as a finite series of half-period cosine (sine) functions onto a half-period sine (cosine) function basis is not finite. We propose new fast methods for computing these complicated projections exactly up to some arbitrary degree using fast Fourier transforms. This method has immediate applications for pseudospectral solutions of many systems of partial differential equations.