Newton's method's basin of attraction for sign-changing solutions of concave and convex nonlinearities

DOI10.1016/J.AMC.2010.08.027zbMath1204.65131OpenAlexW2086954224MaRDI QIDQ613215

Zhao-xiang Li, Hai-Long Zhu

Publication date: 20 December 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.08.027

zbMATH Keywords

convergencenumerical examplesseries expansionbasin of attractionNewton-Raphson methodchaotic behaviorconcave and convex nonlinearitiessign-changing solutionsbifurcation methodnonlinear elliptic eigenvalue problemcontractor iteration method

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical computation of solutions to single equations (65H05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical chaos (65P20) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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