Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation

Chebyshev expansion on intervals with br

Chebyshev expansion on intervals with branch points with application to the root of Kepler’s equation: A Chebyshev–Hermite–Padé method

✍ John P. Boyd 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 976 KB

When two or more branches of a function merge, the Chebyshev series of u(λ) will converge very poorly with coefficients a n of T n (λ) falling as O(1/n α ) for some small positive exponent α. However, as shown in [J.P. Boyd, Chebyshev polynomial expansions for simultaneous approximation of two branc