An efficient predictor-corrector method for solving nonlinear equations
type: Item
instance of: scholarly article
title: An efficient predictor-corrector method for solving nonlinear equations
zbMATH Open document ID: 0632.65054
DOI: 10.1016/0377-0427(87)90203-2
author: N. Sagara
author: Masao Fukushima
published in: Journal of Computational and Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let \(F: {\mathbb{R}}^ n\to {\mathbb{R}}^ n\). The paper presents a new algorithm for obtaining a solution of a nonlinear system of equations \(F(x)=0\). The method is based on the presentation of the system in the form \(H(x,t)=0\) where \(H:{\mathbb{R}}^{n+1}\to {\mathbb{R}}^ n\), \(H(x,1)=F(x)\) and the system \(H(x,0)=0\) has a known solution \(x^ 0\in {\mathbb{R}}^ n\). The predictor- part of the method is an ordinary Euler method, but the corrector-part converges more rapidly than well-known types of the method and of Newton's method. Three different examples are presented which show the efficiency of the algorithm realized in FORTRAN IV. At the convergence criterion \(\epsilon =10^{-6}\) the new method gives the solution from 7 to 41 times faster (by the number of iterates) than the usual Euler method and from 15 to 82 times faster than Newton's method.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 4028760
zbMATH Keywords: continuation method
zbMATH Keywords: FORTRAN IV algorithm
zbMATH Keywords: numerical examples
zbMATH Keywords: predictor- corrector method
zbMATH Keywords: Euler method
zbMATH Keywords: Newton's method
zbMATH Keywords: convergence
describes a project that uses: NSOIA
MaRDI profile type: Publication
full work available at URL: 0377-0427(87)90203-2
OpenAlex ID: W2070066509
cites work: Q3327633
cites work: Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
cites work: On Tracing an Implicitly Defined Curve by Quasi-Newton Steps and Calculating Bifurcation by Local Perturbations
cites work: Q4746734
cites work: Q3925807
cites work: Q5657604
cites work: A globally convergent algorithm for computing fixed points of \(C^2\) maps
description: scientific article; zbMATH DE number 4028760