On the method of modified equations. IV: Numerical techniques based on the modified equation for the Euler forward difference method
type: Item
instance of: scholarly article
title: On the method of modified equations. IV: Numerical techniques based on the modified equation for the Euler forward difference method
zbMATH Open document ID: 0929.65052
DOI: 10.1016/S0096-3003(98)10028-0
published in: Applied Mathematics and Computation
publication date: 2000-01-11T00:00:00Z
review text: The paper is the fourth of a series dealing with the assessment of modified equation methods as a means for the analysis of existing finite difference schemes and for the development of new numerical ones. [For parts III and V see ibid. 103, No.~2-3, 179-212 and 241-285 (1999; reviewed above and below).] The validity of the modified equation based on the third equivalent method (described in the first paper (reviewed above)) is studied as a method for the development on new numerical techniques. Direct-correction techniques are used for the estimation and correction of the truncation error terms in the modified equation. The resulting numerical methods are explicit and their absolute stability is better than that of the original Euler method. The asymptotic successive-correction techniques are applied to the correction of the modified equations. The direct-correction and successive-correction numerical techniques are applied to some systems of ordinary differential equations and are compared with Runge-Kutta techniques.
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1311047
zbMATH Keywords: modified equation methods
zbMATH Keywords: finite difference schemes
zbMATH Keywords: direct-correction techniques
zbMATH Keywords: stability
zbMATH Keywords: asymptotic successive-correction techniques
zbMATH Keywords: systems
zbMATH Keywords: Runge-Kutta techniques
author: Francisco R. Villatoro
author: Juan I. Ramos
reviewed by: Dana Petcu
MaRDI profile type: Publication
cites work: On the method of modified equations. III: Numerical techniques based on the second equivalent equation for the Euler forward difference method
cites work: On the method of modified equations. II: Numerical techniques based on the equivalent equation for the Euler forward difference method
cites work: On the method of modified equations. I: Asymptotic analysis of the Euler forward difference method
cites work: Q3779682
full work available at URL: s0096-3003(98)10028-0
OpenAlex ID: W2134632703
description: scientific article; zbMATH DE number 1311047