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Spectral methods using rational basis functions on an infinite interval

- J. Boyd
- Mathematics
- 1 March 1987

By using the map y = L cot(t) where L is a constant, differential equations on the interval yϵ [− ∞, ∞] can be transformed into tϵ [0, π] and solved by an ordinary Fourier series. In this article,… Expand

The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series

- J. Boyd
- Mathematics
- 1 March 1999

Singular perturbation methods, such as the method of multiple scales and the method of matched asymptotic expansions, give series in a small parameter ε which are asymptotic but (usually) divergent.… Expand

Orthogonal rational functions on a semi-infinite interval

- J. Boyd
- Mathematics
- 1 May 1987

Abstract By applying a mapping to the Chebyshev polynomials, we define a new spectral basis: the “rational Chebyshev functions on the semi-infinite interval,” denoted by TL n ( y ). Continuing… Expand

The Blasius Function in the Complex Plane

- J. Boyd
- Mathematics, Computer Science
- Exp. Math.
- 1999

TLDR

A Comparison of Numerical Algorithms for Fourier Extension of the First, Second, and Third Kinds

- J. Boyd
- Mathematics
- 1 May 2002

The range of Fourier methods can be significantly increased by extending a nonperiodic function f(x) to a periodic function f? on a larger interval. When f(x) is analytically known on the extended… Expand

Equatorial Solitary Waves. Part I: Rossby Solitons

- J. Boyd
- Physics
- 1 November 1980

Abstract Using the method of multiple scales, I show that long, weakly nonlinear, equatorial Rossby waves are governed by either the Korteweg-deVries (KDV) equation (symmetric modes of odd mode… Expand

The Blasius Function: Computations Before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems

- J. Boyd
- Mathematics, Computer Science
- SIAM Rev.
- 1 November 2008

TLDR

The Optimization of Convergence for Chebyshev Polynomial Methods in an Unbounded Domain

- J. Boyd
- Mathematics
- 1982

By using the method of steepest descent, I have compared the suitability of three different methods for solving problems in a semi-infinite or infinite domain using Chebyshev polynomials. Exponential… Expand

Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudospectral algorithms

- J. Boyd
- Mathematics
- 20 September 2004

Prolate spheroidal functions of order zero are generalizations of Legendre polynomials which, when the "bandwidth parameter" c > 0, oscillate more uniformly on x ∈ [-1,1] than either Chebyshev or… Expand

Pade´ approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain

- J. Boyd
- Mathematics
- 1 May 1997

We describe a four-step algorithm for solving ordinary differential equation nonlinear boundary-value problems on infinite or semi-infinite intervals. The first step is to compute high-order Taylor… Expand

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