Rootfinding for a transcendental equation without a first guess: polynomialization of Kepler's equation through Chebyshev polynomial expansion of the sine

DOI10.1016/j.apnum.2005.11.010zbMath1105.65054OpenAlexW2081192208WikidataQ61893610 ScholiaQ61893610MaRDI QIDQ857020

John P. Boyd

Publication date: 14 December 2006

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2005.11.010

zbMATH Keywords

celestial mechanicselliptical orbitMatlab implementationtranscendental equationsChebysbev expansions

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Numerical computation of solutions to single equations (65H05) Celestial mechanics (70F15)

Related Items

Chebyshev expansion on intervals with branch points with application to the root of Kepler's equation: A Chebyshev-Hermite-Padé method, Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding, A novel cubically convergent iterative method for computing complex roots of nonlinear equations, Kepler's equation and limit cycles in a class of PWM feedback control systems, New series for the cosine lemniscate function and the polynomialization of the lemniscate integral, Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind

Uses Software

• Matlab

Cites Work

• Some remarks on multivariate Chebyshev polynomials
• The convergence of Newton-Raphson iteration with Kepler's equation
• Global convergence of Newton's method on an interval
• A Chebyshev polynomial interval-searching method (``Lanczos economization) for solving a nonlinear equation with application to the nonlinear eigenvalue problem
• Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves
• Computing real roots of a polynomial in Chebyshev series form through subdivision
• The special functions and their approximations. Vol. I, II
• Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding
• Numerical Polynomial Algebra
• Roots of Polynomials Expressed in Terms of Orthogonal Polynomials
• Analysis of Some Padé--Chebyshev Approximants
• Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions
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