A variable-stepsize variable-order multistep method for the integration of perturbed linear problems

Authors:
David J. López;Pablo Martín;Amelia García
Affiliations:
Departmento de Mathemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Paseo Alfonsa XIII, 30203 Cartagena, Spain;Departamento de Matemática Aplicada a la Ingeniería, E.T.S. de Ingenieros Industriales, Univerisdad de Valladolid, Paseo del Cauce s/n, 47011 Valladolid, Spain;Departamento de Matemática Aplicada a la Ingeniería, E.T.S. de Ingenieros Industriales, Univerisdad de Valladolid, Paseo del Cauce s/n, 47011 Valladolid, Spain
Venue:
Applied Numerical Mathematics
Year:
2002

Citing 4
Cited 0

Numerical methods for ordinary differential systems: the initial value problem

Numerical methods for ordinary differential systems: the initial value problem
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Multistep Numerical Methods Based on the Scheifele G-Functions with Application to Satellite Dynamics

SIAM Journal on Numerical Analysis
A numerical method for the integration of perturbed linear problems

Applied Mathematics and Computation

Quantified Score

Hi-index	0.01

Visualization

Abstract

In 1971 Scheifele wrote the solution of a perturbed oscillator as an expansion in terms of a new set of functions, which extends the monomials in the Taylor series of the solution. Recently, Martín and Ferrándiz constructed a multistep code based on the Scheifele technique, and it was generalized by López and Martín for perturbed linear problems. However, the remarked codes are constant steplength methods, and efficient integrators must be able to change the steplength. In this paper we extend the ideas of Krogh from Adams methods to the algorithm proposed by López and Martín, and we show the advantages of the new code in perturbed problems.