417 results on '"John P. Boyd"'
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2. Asymptotic Coefficients and Errors for Chebyshev Polynomial Approximations with Weak Endpoint Singularities: Effects of Different Bases.
3. When integration sparsification fails: Banded Galerkin discretizations for Hermite functions, rational Chebyshev functions and sinh-mapped Fourier functions on an infinite domain, and Chebyshev methods for solutions with C∞ endpoint singularities.
4. Exact solutions to a nonlinear partial differential equation: The Product-of-Curvatures Poisson (uxxuyy=1).
5. Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides.
6. The Crane equation uuxx=-2: The general explicit solution and a case study of Chebyshev polynomial series for functions with weak endpoint singularities.
7. New approximations to the principal real-valued branch of the Lambert W-function.
8. Convergent Power Series for Boundary Value Problems and Eigenproblems with Application to Atmospheric and Oceanic Tides.
9. All roots spectral methods: Constraints, floating point arithmetic and root exclusion.
10. Five themes in Chebyshev spectral methods applied to the regularized Charney eigenproblem: Extra numerical boundary conditions, a boundary-layer-resolving change of coordinate, parameterizing a curve which is singular at an endpoint, extending the tau method to log-and-polynomials and finding the roots of a polynomial-and-log approximation.
11. Bandwidth truncation for Chebyshev polynomial and ultraspherical/Chebyshev Galerkin discretizations of differential equations: Restrictions and two improvements.
12. High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences.
13. Tracing Multiple Solution Branches for Nonlinear Ordinary Differential Equations: Chebyshev and Fourier Spectral Methods and a Degree-Increasing Spectral Homotopy [DISH].
14. Correcting Three Errors in Kantorovich & Krylov's Approximate Methods of Higher Analysis.
15. A degree-increasing [N to N+1] homotopy for Chebyshev and Fourier spectral methods.
16. Spectral methods in non-tensor geometry, Part II: Chebyshev versus Zernike polynomials, gridding strategies and spectral extension on squircle-bounded and perturbed-quadrifolium domains.
17. A Fourier error analysis for radial basis functions and the Discrete Singular Convolution on an infinite uniform grid, Part 1: Error theorem and diffusion in Fourier space.
18. RBF-vortex methods for the barotropic vorticity equation on a sphere.
19. Adaptive radial basis function and Hermite function pseudospectral methods for computing eigenvalues of the prolate spheroidal wave equation for very large bandwidth parameter.
20. Modal preconditioning of Galerkin spectral methods: Dual bookkeeping for the Delves-Freeman iteration.
21. Chebyshev-Fourier spectral methods in bipolar coordinates.
22. Approximation on non-tensor domains including squircles, Part III: Polynomial hyperinterpolation and radial basis function interpolation on Chebyshev-like grids and truncated uniform grids.
23. Four ways to compute the inverse of the complete elliptic integral of the first kind.
24. Optimal Truncations for Multivariate Fourier and Chebyshev Series: Mysteries of the Hyperbolic Cross: Part I: Bivariate Case.
25. The Fourier Transform of the quartic Gaussian exp(-Ax4): Hypergeometric functions, power series, steepest descent asymptotics and hyperasymptotics and extensions to exp(-Ax2n).
26. Accurate calculation of the solutions to the Thomas-Fermi equations.
27. Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the D4 symmetry group; Interpolation within a squircle, Part I.
28. The Relationships Between Chebyshev, Legendre and Jacobi Polynomials: The Generic Superiority of Chebyshev Polynomials and Three Important Exceptions.
29. Quartic Gaussian and Inverse-Quartic Gaussian radial basis functions: The importance of a nonnegative Fourier transform.
30. A Fourier error analysis for radial basis functions on an infinite uniform grid. Part 2: Spectral-plus is special.
31. Rational Chebyshev series for the Thomas-Fermi function: Endpoint singularities and spectral methods.
32. A comparison of companion matrix methods to find roots of a trigonometric polynomial.
33. Finding the Zeros of a Univariate Equation: Proxy Rootfinders, Chebyshev Interpolation, and the Companion Matrix.
34. The Nonconvergence of $$h$$ h -Refinement in Prolate Elements.
35. Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind.
36. Parity symmetry with respect to both x=0 and x=L requires periodicity with period 4L: Connections between computer graphics, group theory and spectral methods for solving partial differential equations.
37. Computing the real roots of a Fourier series-plus-linear-polynomial: A Chebyshev companion matrix approach.
38. Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions.
39. Isospectral heterogeneous domains: A numerical study.
40. One-point pseudospectral collocation for the one-dimensional Bratu equation.
41. New series for the cosine lemniscate function and the polynomialization of the lemniscate integral.
42. Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier Series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions.
43. The near-equivalence of five species of spectrally-accurate radial basis functions (RBFs): Asymptotic approximations to the RBF cardinal functions on a uniform, unbounded grid.
44. Six strategies for defeating the Runge Phenomenon in Gaussian radial basis functions on a finite interval.
45. Asymptotic coefficients for Gaussian radial basis function interpolants.
46. The Legendre-Burgers equation: When artificial dissipation fails.
47. Error saturation in Gaussian radial basis functions on a finite interval.
48. The uselessness of the Fast Gauss Transform for summing Gaussian radial basis function series.
49. Computing continuous core/periphery structures for social relations data with MINRES/SVD.
50. Divergence (Runge Phenomenon) for least-squares polynomial approximation on an equispaced grid and Mock-Chebyshev subset interpolation.
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