Record Details

ON NAIVE TAYLOR MODEL INTEGRATION METHOD

Baghdad Science Journal


Field	Value

Title	ON NAIVE TAYLOR MODEL INTEGRATION METHOD

Creator	Journal, Baghdad Science

Description	Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an effective tool for reducing both the dependency problem and the wrapping effect. By construction, Taylor model methods appear particularly suitable for integrating nonlinear ODEs. In this paper, we analyze Taylor model based integration of ODEs and compare Taylor model with traditional enclosure methods for IVPs for ODEs. More advanced Taylor model integration methods are discussed in the algorithm (1). For clarity, we summarize the major steps of the naive Taylor model method as algorithm 1.

Publisher	College of Science for Women - University of Baghdad

Date	2009-03-01

Type	info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Peer-reviewed Article

Format	application/pdf

Identifier	http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/973

Source	مجلة بغداد للعلوم; مجلد 6 عدد 1 (2009): issue 1; 222-230 Baghdad Science Journal; Vol 6 No 1 (2009): issue 1; 222-230 2411-7986 2078-8665

Language	eng

Relation	http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/973/904

Rights	Copyright (c) 2009 Baghdad Science Journal