Choice of an initial guess for Newton's method to solve nonlinear differential equations

Hayoung Choi; Sang Dong Kim; Byeong Chun Shin

doi:10.1016/j.camwa.2022.04.013

Choice of an initial guess for Newton's method to solve nonlinear differential equations

Hayoung Choi
, Sang Dong Kim
, Byeong Chun Shin

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

A proper initial guess is critical for implementing Newton's iteration to approximate an exact solution of a nonlinear differential equation like the Navier-Stokes equations or magnetohydrodynamic equations. In this article, we will provide a theoretical criteria for the way of choosing an initial guess required for Newton's iteration for approximating an exact solution of a nonlinear differential equation.

Original language	English
Pages (from-to)	69-73
Number of pages	5
Journal	Computers and Mathematics with Applications
Volume	117
DOIs	https://doi.org/10.1016/j.camwa.2022.04.013
State	Published - 1 Jul 2022

Keywords

Initial guess
Newton's method
Nonlinear differential equation

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10.1016/j.camwa.2022.04.013

Cite this

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title = "Choice of an initial guess for Newton's method to solve nonlinear differential equations",

abstract = "A proper initial guess is critical for implementing Newton's iteration to approximate an exact solution of a nonlinear differential equation like the Navier-Stokes equations or magnetohydrodynamic equations. In this article, we will provide a theoretical criteria for the way of choosing an initial guess required for Newton's iteration for approximating an exact solution of a nonlinear differential equation.",

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AU - Choi, Hayoung

AU - Kim, Sang Dong

AU - Shin, Byeong Chun

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N2 - A proper initial guess is critical for implementing Newton's iteration to approximate an exact solution of a nonlinear differential equation like the Navier-Stokes equations or magnetohydrodynamic equations. In this article, we will provide a theoretical criteria for the way of choosing an initial guess required for Newton's iteration for approximating an exact solution of a nonlinear differential equation.

AB - A proper initial guess is critical for implementing Newton's iteration to approximate an exact solution of a nonlinear differential equation like the Navier-Stokes equations or magnetohydrodynamic equations. In this article, we will provide a theoretical criteria for the way of choosing an initial guess required for Newton's iteration for approximating an exact solution of a nonlinear differential equation.

KW - Initial guess

KW - Newton's method

KW - Nonlinear differential equation

UR - https://www.scopus.com/pages/publications/85129371739

U2 - 10.1016/j.camwa.2022.04.013

DO - 10.1016/j.camwa.2022.04.013

M3 - Article

AN - SCOPUS:85129371739

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VL - 117

SP - 69

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

ER -

Choice of an initial guess for Newton's method to solve nonlinear differential equations

Abstract

Keywords

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