1996/12/05 by Bogdan I. Epureanu, Epureanu, Bogdan I., Henry Greenside +1 · 1 citation
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.chao-dyn/9612010
openalex publication_date 1996/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An intriguing and unexpected result for students learning numerical analysis is that Newton's method, applied to the simple polynomial z3 - 1 = 0 in the complex plane, leads to intricately interwoven basins of attraction of the roots. As an example of an interesting open question that may help to stimulate student interest in numerical analysis, we investigate the question of whether a damping method, which is designed to increase the likelihood of convergence for Newton's method, modifies the fractal structure of the basin boundaries. The overlap of the frontiers of numerical analysis and nonlinear dynamics provides many other problems that can help to make numerical analysis courses interesting.