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Spectral methods using rational basis functions on an infinite interval
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
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
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 ). ContinuingExpand
The Blasius Function in the Complex Plane
  • J. Boyd
  • Mathematics, Computer Science
  • Exp. Math.
  • 1999
The Blasius function, denoted by f, is the solution to a simple nonlinear boundary layer problem, a third order ordinary differential equation on x ∈ [0, ∞]. Expand
A Comparison of Numerical Algorithms for Fourier Extension of the First, Second, and Third Kinds
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 extendedExpand
Equatorial Solitary Waves. Part I: Rossby Solitons
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 modeExpand
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
The Blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick, semi-infinite flat plate. Expand
The Optimization of Convergence for Chebyshev Polynomial Methods in an Unbounded Domain
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. ExponentialExpand
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 orExpand
Pade´ approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain
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 TaylorExpand