On the efficiency of Newton and Broyden numerical methods in the investigation of the regular polygon problem of (\(N + 1\)) bodies

DOI10.1016/j.amc.2009.02.015zbMath1168.65358OpenAlexW2056038648MaRDI QIDQ1026269

Maria Gousidou-Koutita, Telemachus J. Kalvouridis

Publication date: 24 June 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.02.015

zbMATH Keywords

celestial mechanicsNewton and quasi-Newton methods\((N + 1)\)-ring-body problemcomparison of numerical methodsnon-linear algebraic equations

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10)

Related Items (5)

Equilibrium points and basins of convergence in the linear restricted four-body problem with angular velocity ⋮ Investigating the Newton-Raphson basins of attraction in the restricted three-body problem with modified Newtonian gravity ⋮ Periodic motions and their stability in a \(N=\nu+1\)-body regular polygonal configuration ⋮ On the efficiency of Newton and Broyden numerical methods in the investigation of the regular polygon problem of (\(N + 1\)) bodies ⋮ Basins of Convergence of Equilibrium Points in the Generalized Hill Problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Numerov-type method for the numerical solution of the radial Schrödinger equation
• A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrödinger equation
• On the efficiency of Newton and Broyden numerical methods in the investigation of the regular polygon problem of (\(N + 1\)) bodies
• A rapid generalized method of bisection for solving systems of non-linear equations
• A comparison of numerical integration methods in the equatorial magnetic- binary problem
• On a particular restricted five-body problem. An analysis with computer algebra
• Application of high-order Runge-Kutta methods in the magnetic-binary problem
• An explicit almost \(P\)-stable two-step method with phase-lag of order infinity for the numerical integration of second-order periodic initial- value problems
• On the efficiency of Runge-Kutta-Nyström methods with interpolants for solving equations of the form \(Y=F(T,Y,Y')\) over short timespans
• Explicit high order methods for the numerical integration of periodic initial-value problems
• Explicit exponentially fitted methods for the numerical solution of the Schrödinger equation
• A planar case of the \(n+1\) body problem: The ring problem
• Some new variable-step methods with minimal phase lag for the numerical integration of special second-order initial-value problem
• Modified Runge-Kutta methods for the numerical solution of ODEs with oscillating solutions
• A new finite difference scheme with minimal phase-lag for the numerical solution of the Schrödinger equation.
• A \(P\)-stable exponentially fitted method for the numerical integration of the Schrödinger equation
• Embedded eighth order methods for the numerical solution of the Schrödinger equation
• An optimized Runge-Kutta method for the solution of orbital problems
• High algebraic, high phase-lag order embedded Numerov-type methods for oscillatory problems
• Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation
• A NEW NUMEROV-TYPE METHOD FOR COMPUTING EIGENVALUES AND RESONANCES OF THE RADIAL SCHRÖDINGER EQUATION

This page was built for publication: On the efficiency of Newton and Broyden numerical methods in the investigation of the regular polygon problem of (\(N + 1\)) bodies