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A Class of Hybrid Methods for Direct Integration of Fourth-Order Ordinary Differential Equations

A Class of Hybrid Methods for Direct Integration of Fourth-Order Ordinary Differential Equations A class of hybrid methods for solving fourth-order ordinary differential equations (HMFD) is proposed and investigated. Using the theory of B-series, we study the order of convergence of the HMFD methods. The main result is a set of order conditions, analogous to those for two-step hybrid method, which offers a better alternative to the usual ad hoc Taylor expansions. Based on the algebraic order conditions, a one-stage and two-stage explicit HMFD methods are constructed. Results from numerical experiment suggest the superiority of the new methods in terms of accuracy and computational efficiency over hybrid methods for special second ODEs, Runge–Kutta methods recently proposed for solving special fourth-order ODEs directly and some linear multistep methods proposed for the same purpose in the literature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Malaysian Mathematical Sciences Society Springer Journals

A Class of Hybrid Methods for Direct Integration of Fourth-Order Ordinary Differential Equations

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References (17)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
0126-6705
eISSN
2180-4206
DOI
10.1007/s40840-017-0520-x
Publisher site
See Article on Publisher Site

Abstract

A class of hybrid methods for solving fourth-order ordinary differential equations (HMFD) is proposed and investigated. Using the theory of B-series, we study the order of convergence of the HMFD methods. The main result is a set of order conditions, analogous to those for two-step hybrid method, which offers a better alternative to the usual ad hoc Taylor expansions. Based on the algebraic order conditions, a one-stage and two-stage explicit HMFD methods are constructed. Results from numerical experiment suggest the superiority of the new methods in terms of accuracy and computational efficiency over hybrid methods for special second ODEs, Runge–Kutta methods recently proposed for solving special fourth-order ODEs directly and some linear multistep methods proposed for the same purpose in the literature.

Journal

Bulletin of the Malaysian Mathematical Sciences SocietySpringer Journals

Published: Jun 27, 2017

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