Publication detail

Predictor–corrector Obreshkov pairs

SEHNALOVÁ, P. BUTCHER, J.

Original Title

Predictor–corrector Obreshkov pairs

Type

journal article - other

Language

English

Original 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.

Keywords

PEC methods, Adams methods, Nordsieck representation, Ordinary differential equations, Numerical methods

Authors

SEHNALOVÁ, P.; BUTCHER, J.

RIV year

2013

Released

10. 1. 2013

Publisher

Springer-Verlag Wien

Location

AT

ISBN

0010-485X

Periodical

COMPUTING

Year of study

95

Number

5

State

Republic of Austria

Pages from

355

Pages to

371

Pages count

17

URL

http://link.springer.com/article/10.1007%2Fs00607-012-0258-0

BibTex

@article{BUT97130,
  author="Pavla {Sehnalová} and John {Butcher}",
  title="Predictor–corrector Obreshkov pairs",
  journal="COMPUTING",
  year="2013",
  volume="95",
  number="5",
  pages="355--371",
  doi="10.1007/s00607-012-0258-0",
  issn="0010-485X",
  url="http://link.springer.com/article/10.1007%2Fs00607-012-0258-0"
}