Quasi-\(L^{p}\) norm orthogonal Galerkin expansions in sums of Jacobi polynomials

DOI10.1007/s11075-009-9353-5zbMath1197.65027OpenAlexW2029055820MaRDI QIDQ5961881

Philip W. Livermore, Glenn R. Ierley

Publication date: 16 September 2010

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-009-9353-5

zbMATH Keywords

spectral methodexponential convergenceorthogonal polynomialauto-orthogonalityGalerkin expansionGram-Schmidt methodJacobi polynomial

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Computation of special functions and constants, construction of tables (65D20) Numerical approximation and evaluation of special functions (33F05)

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An optimal Galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere ⋮ Tensor calculus in spherical coordinates using Jacobi polynomials. I: Mathematical analysis and derivations ⋮ A Jacobi-Jacobi dual-Petrov-Galerkin method for third- and fifth-order differential equations ⋮ Optimal kinematic dynamos in a sphere ⋮ An efficient direct solver for multidimensional elliptic Robin boundary value problems using a Legendre spectral-Galerkin method ⋮ A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations ⋮ New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method ⋮ Galerkin orthogonal polynomials ⋮ Taylor state dynamos found by optimal control: axisymmetric examples ⋮ The optimal kinematic dynamo driven by steady flows in a sphere ⋮ 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

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