Extension of Chebfun to periodic functions

TL;DR

This paper extends the Chebfun framework to handle periodic functions using trigonometric polynomial approximations, enabling high-precision numerical solutions to periodic differential equations.

Contribution

It introduces algorithms and mathematical methods for periodic function approximation within Chebfun, highlighting differences from the nonperiodic case.

Findings

Achieves approximations to machine precision for periodic functions.

Provides algorithms for solving linear and nonlinear periodic ODEs.

Highlights key differences from nonperiodic Chebyshev methods.

Abstract

Algorithms and underlying mathematics are presented for numerical computation with periodic functions via approximations to machine precision by trigonometric polynomials, including the solution of linear and nonlinear periodic ordinary differential equations. Differences from the nonperiodic Chebyshev case are highlighted.