Newton-homotopy analysis method for nonlinear equations

DOI10.1016/j.amc.2006.11.136zbMath1119.65032OpenAlexW2086285205MaRDI QIDQ2372061

Yue Tan, Shi-Jun Liao, Saeid Abbasbandy

Publication date: 10 July 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.11.136

zbMATH Keywords

numerical examplesNewton-Raphson methodAdomian's decomposition methodhomotopy analysis methodhomotopy perturbation method

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Numerical computation of solutions to single equations (65H05)

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Cites Work

• Unnamed Item
• Exact flow of a third grade fluid past a porous plate using homotopy analysis method
• On the explicit analytic solutions of an Oldroyd 6-constant fluid
• Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid
• An explicit, totally analytic approximate solution for Blasius' viscous flow problems
• A new branch of solutions of boundary-layer flows over an impermeable stretched plate
• Solving frontier problems of physics: the decomposition method
• Convergence of Adomian's method applied to nonlinear equations
• A kind of approximation solution technique which does not depend upon small parameters. II: An application in fluid mechanics
• Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method
• On the homotopy analysis method for nonlinear problems.
• Explicit analytic solution for similarity boundary layer equations.
• Historical developments in convergence analysis for Newton's and Newton-like methods
• Couette and Poiseuille flows of an Oldroyd 6-constant fluid with magnetic field
• Comparison of homotopy perturbation method and homotopy analysis method
• An approximate solution technique not depending on small parameters: A special example
• Homotopy perturbation technique
• Modified homotopy perturbation method for nonlinear equations and comparison with Adomian decomposition method
• Homotopy solutions for a generalized second-grade fluid past a porous plate
• Comparison between the homotopy analysis method and homotopy perturbation method
• On nonlinear flows with slip boundary condition
• Newton‐like iteration methods for solving non‐linear equations
• A method for solving nonlinear equations
• New high-order convergence iteration methods without employing derivatives for solving nonlinear equations

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