NDLI: Predictor–corrector Obreshkov pairs

Content Provider	Springer Nature Link
Author	Sehnalová, Pavla Butcher, John C.
Copyright Year	2013
Abstract	The combination of predictor–corrector (PEC) pairs of Adams methods can be generalized to high derivative methods using Obreshkov quadrature formulae. It is convenient to construct predictor–corrector pairs using a combination of explicit (Adams–Bashforth for traditional PEC methods) and implicit (Adams–Moulton for traditional PEC methods) forms of the methods. This paper will focus on one special case of a fourth order method consisting of a two-step predictor followed by a one-step corrector, each using second derivative formulae. There is always a choice in predictor–corrector pairs of the so-called mode of the method and we will consider both PEC and PECE modes. The Nordsieck representation of Adams methods, as developed by C. W. Gear and others, adapts well to the multiderivative situation and will be used to make variable stepsize convenient. In the first part of the paper we explain the basic approximations used in the predictor–corrector formula. Those can be written in terms of Obreshkov quadrature. Next section we discuss the equations in terms of Nordsieck vectors. This provides an opportunity to extend the Gear Nordsieck factorization to achieve a variable stepsize formulation. Numerical tests with the new method are also discussed. The paper will present Prothero–Robinson and Kepler problem to illustrate the power of the approach.
Ending Page	371
Page Count	17
Starting Page	355
File Format	PDF
ISSN	0010485X
e-ISSN	14365057
Journal	Computing
Issue Number	5
Volume Number	95
Language	English
Publisher	Springer Vienna
Publisher Date	2013-01-10
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multistep, Runge-Kutta and extrapolation methods Software Engineering PEC methods Numerical methods Computer Application in Administrative Data Processing Computer Science Nordsieck representation Ordinary differential equations Artificial Intelligence (incl. Robotics) Information Systems Applications (incl. Internet) Adams methods Computer Communication Networks
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Computational Mathematics Numerical Analysis Computer Science Applications Software

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