On the method of modified equations. VI: Asymptotic analysis of and asymptotic successive-corrections techniques for two-point, boundary-value problems in ODE's
type: Item
instance of: scholarly article
title: On the method of modified equations. VI: Asymptotic analysis of and asymptotic successive-corrections techniques for two-point, boundary-value problems in ODE's
zbMATH Open document ID: 1030.65085
DOI: 10.1016/S0096-3003(98)10099-1
published in: Applied Mathematics and Computation
publication date: 2000-06-25T00:00:00Z
review text: [For part V see ibid. 103, 241-285 (1999; Zbl 0929.65053).] The sixth paper in the series concerning the method of modified equations extends it to two-point boundary-value problems in ordinary differential equations, and the implicit centered finite difference scheme is considered as example. The proposed methods are applied to homogeneous and non-homogeneous, second-order, linear and nonlinear ordinary differential equations. Three kinds of modified equations, i.e. the equivalent, second equivalent and simply modified equations, are analyzed and it is shown that they are asymptotically equivalent when the equivalent equation is used for the boundary conditions. Furthermore, asymptotic successive-corrections techniques are applied to the three kinds of modified equations to obtain higher-order schemes. The results of the proposed techniques are compared for several second-order ordinary differential equations. The numerical order, the errors and the computational cost are also studied.
reviewed by: Dana Petcu
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65L70
zbMATH DE Number: 1464446
zbMATH Keywords: asymptotic successive-corrections techniques
zbMATH Keywords: two-point boundary-value problems
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: error bounds
zbMATH Keywords: comparison of methods
zbMATH Keywords: method of modified equations
zbMATH Keywords: implicit centered finite difference scheme
author: Francisco R. Villatoro
author: Juan I. Ramos
MaRDI profile type: Publication
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full work available at URL: s0096-3003(98)10099-1
OpenAlex ID: W2146001979
description: scientific article; zbMATH DE number 1464446