Selective solutions to transcendental equations

DOI10.1016/0898-1221(91)90207-KzbMath0753.65038OpenAlexW1966086073MaRDI QIDQ1192158

Nasser Doual, Rémi Vaillancourt, James Lucien Howland

Publication date: 27 September 1992

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(91)90207-k

zbMATH Keywords

fixed pointsNewton's methodConvergenceattractive cyclesinverse iterationFatou-Julia theoryFatou-Julia setglobal iterative methodsroots of elementary transcendental equationsunpredictable roots

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical computation of solutions to single equations (65H05)

Related Items (2)

Iteration of meromorphic functions ⋮ Computer solution of the scattering problem for a groove in a metallic plane using the modal method

Cites Work

• Attractive cycles in the iteration of meromorphic functions
• A new class of quite elementary closed-form integral formulae for roots of nonlinear equations
• Complex analytic dynamics on the Riemann sphere
• The hyperbolic Kepler equation (and the elliptic equation revisited)
• My Favorite Proof of Mehler's Integral
• Comparing Numerical Methods for Ordinary Differential Equations
• An exact analytical solution of Kepler's equation
• On the Iteration of analytic functions .
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