research-article

A Code Based on the Two-Stage Runge-Kutta Gauss Formula for Second-Order Initial Value Problems

Authors:

Severiano González-Pinto,

Rogel Rojas-BelloAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 37, Issue 3

Article No.: 25, Pages 1 - 30

https://doi.org/10.1145/1824801.1824803

Published: 01 September 2010 Publication History

Abstract

A code based on the two-stage Gauss formula (order four) for second-order initial value problems of a special type is developed. This code can be used to obtain a low- to medium-precision integration for a wide range of problems in the class of oscillatory type, Hamiltonian problems, and time-dependent partial differential equations discretized in space by finite differences or finite elements. The iteration process used in solving for the stage values of the Gauss formula, the selection of the initial step size, and the choice of an appropriate local error estimator for determining the step size change according to a particular tolerance specified by the user are studied. Moreover, a global error estimate and a dense output at equidistant points in the integration interval are supplied with the code. Numerical experiments and some comparisons with certain standard codes on relevant test problems are also given.

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Cited By

Sunday JShokri AMahwash Kamoh NCleofas Dang BIdrisoglu Mahmudov N(2024)A computational approach to solving some applied rigid second-order problemsMathematics and Computers in Simulation10.1016/j.matcom.2023.10.019217(121-138)Online publication date: Mar-2024
https://doi.org/10.1016/j.matcom.2023.10.019
Lei XWang YWang XLin GQin X(2022)A High-Accurate Time Integration Method for Solving Structural Vibration ResponsesMathematical Problems in Engineering10.1155/2022/35633932022(1-8)Online publication date: 2-Nov-2022
https://doi.org/10.1155/2022/3563393

Index Terms

A Code Based on the Two-Stage Runge-Kutta Gauss Formula for Second-Order Initial Value Problems
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 37, Issue 3

September 2010

296 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1824801

Issue’s Table of Contents

Copyright © 2010 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 01 September 2010

Accepted: 01 November 2009

Revised: 01 October 2009

Received: 01 September 2005

Published in TOMS Volume 37, Issue 3

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Cited By

Sunday JShokri AMahwash Kamoh NCleofas Dang BIdrisoglu Mahmudov N(2024)A computational approach to solving some applied rigid second-order problemsMathematics and Computers in Simulation10.1016/j.matcom.2023.10.019217(121-138)Online publication date: Mar-2024
https://doi.org/10.1016/j.matcom.2023.10.019
Lei XWang YWang XLin GQin X(2022)A High-Accurate Time Integration Method for Solving Structural Vibration ResponsesMathematical Problems in Engineering10.1155/2022/35633932022(1-8)Online publication date: 2-Nov-2022
https://doi.org/10.1155/2022/3563393

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