IMPLEMENTATION OF EXPLICIT NORDSIECK METHODS WITH INHERENT QUADRATIC STABILITY-Reference-Cited by-同舟云学术

IMPLEMENTATION OF EXPLICIT NORDSIECK METHODS WITH INHERENT QUADRATIC STABILITY

Published:2013-04-01 Issue:2 Volume:18 Page:289-307
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Bras Michel¹,Cardone Angelamaria²,D'Ambrosio Raffaele²

Affiliation:

1. AGH University of Science and Technology, Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland; Jagiellonian University, Faculty of Mathematics and Computer Science ul. prof. S. Lojasiewicza 6, 30-348 Krakow, Poland

2. Universita degli Studi di Salerno via Ponte Don Melillo, I-84084 Fisciano (SA), Italy

Abstract

The present paper deals with the implementation in a variable-step algorithm of general linear methods in Nordsieck form with inherent quadratic stability and large stability regions constructed recently by Braś and Cardone. Various implementation issues such as rescale strategy, local error estimation, step-changing strategy and starting procedure are discussed. Some numerical experiments are reported, which show the performances of the methods and make comparisons with other existing methods.

Publisher

Vilnius Gediminas Technical University

Subject

Modelling and Simulation,Analysis

Reference21 articles.

1. Nordsieck representation of two-step Runge–Kutta methods for ordinary differential equations

2. Explicit Nordsieck methods with extended stability regions

3. NORDSIECK METHODS WITH INHERENT QUADRATIC STABILITY

4. CONSTRUCTION OF EFFICIENT GENERAL LINEAR METHODS FOR NON-STIFF DIFFERENTIAL SYSTEMS

5. Numerical Methods for Ordinary Differential Equations

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