Piecewise-linearized methods for initial-value problems
type: Item
instance of: scholarly article
title: Piecewise-linearized methods for initial-value problems
zbMATH Open document ID: 0870.65066
DOI: 10.1016/S0096-3003(96)00040-9
author: C. M. García-López
author: Juan I. Ramos
published in: Applied Mathematics and Computation
publication date: 1997-09-22T00:00:00Z
review text: Piecewise-linearized methods for the solution of initial value problems in ordinary differential equations are developed by approximating the right-hand sides of the equations by means of a Taylor polynomial of degree one. The resulting approximation can be integrated analytically to obtain the solution in each interval, and yields the exact solution for linear problems. Three adaptive methods, based on the norm of the Jacobian matrix, maintaining constant the value of the approximation errors made by the linearization, and Richardson extrapolation are considered. Numerical experiments with some nonstiff first- and second-order equations suggest that the accuracy of the piecewise-linearized methods is superior to that of the explicit, modified, or second-order Euler method, or the trapezoidal rule, but less than that of the fourth-order Runge-Kutta method.
reviewed by: Michael Sever
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L12
zbMATH DE Number: 1006498
zbMATH Keywords: finite difference methods
zbMATH Keywords: piecewise-linearized methods
zbMATH Keywords: comparison of methods
zbMATH Keywords: numerical experiments
zbMATH Keywords: adaptive methods
zbMATH Keywords: linearization
zbMATH Keywords: Richardson extrapolation
zbMATH Keywords: Euler method
zbMATH Keywords: Runge-Kutta method
MaRDI profile type: Publication
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full work available at URL: s0096-3003(96)00040-9
OpenAlex ID: W2017996934
description: scientific article; zbMATH DE number 1006498