Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim

DOI10.1016/j.camwa.2010.09.040zbMath1207.65059OpenAlexW2036980208MaRDI QIDQ630668

Juan-Miguel Gracia

Publication date: 19 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.09.040

zbMATH Keywords

Newton-Raphson methodfractalshelicoptersystem of nonlinear algebraic equationsaeroelastic analysis

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Control of mechanical systems (70Q05) Fractals (28A80) Dynamics of multibody systems (70E55) Systems arising from the discretization of structural vibration problems (70J50)

Related Items (2)

Fractal dimension and Wada measure revisited: no straightforward relationships in NDDS ⋮ Estimating the Hausdorff-Besicovitch dimension of boundary of basin of attraction in helicopter trim

Cites Work

• Unnamed Item
• Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations
• Conjugate direction particle swarm optimization solving systems of nonlinear equations
• A general theory of rotorcraft trim
• On Newton-type methods with cubic convergence
• A multidisciplinary optimization using semi-analytical sensitivity analysis procedure and multilevel decomposition
• The Julia set of Newton's method for multiple root
• Newton-homotopy analysis method for nonlinear equations
• Discontinuous Galerkin finite element in time for solving periodic differential equations
• Newton's method for the Navier-Stokes equations with finite element initial guess of Stokes equations
• A non-iterative method for solving non-linear equations
• Solving the nonlinear equations by the Newton-homotopy continuation method with adjustable auxiliary homotopy function
• Dynamic Stability of a Rotor Blade Using Finite Element Analysis
• Nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations
• Newton’s method on the complex exponential function
• Fractal Basins of Attraction Associated with a Damped Newton's Method
• An optimization approach to vibration reduction in helicopter rotors with multiple active trailing edge flaps
• New high-order convergence iteration methods without employing derivatives for solving nonlinear equations

This page was built for publication: Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim