Construction of Runge–Kutta type methods for solving ordinary differential equations

In this paper, we study Runge–Kutta methods with continuous stage, introduced by Butcher in 1987. By setting the coefficients of this family of methods and choosing the appropriate numerical integration, we derive new classes of Runge–Kutta methods. Furthermore, we extend the W-transformation techni...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics and computation Vol. 234; pp. 179 - 191
Main Authors: Tang, Wensheng, Sun, Yajuan
Format: Journal Article
Language:English
Published: Elsevier Inc 15.05.2014
Subjects:
(Conjugate) Symplectic method
Computation
Conjugates
Construction
Differential equations
Energy-preserving method
Hamiltonian system
Mathematical models
Numerical integration
Runge-Kutta method
Runge–Kutta method with continuous stage
Symmetric method
W-transformation
Energy-preserving method
Hamiltonian system
(Conjugate) Symplectic method
Runge–Kutta method with continuous stage
Symmetric method
W-transformation
ISSN:0096-3003, 1873-5649
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we study Runge–Kutta methods with continuous stage, introduced by Butcher in 1987. By setting the coefficients of this family of methods and choosing the appropriate numerical integration, we derive new classes of Runge–Kutta methods. Furthermore, we extend the W-transformation technique by permitting W to be a non-square matrix. This allows us to construct more high-order implicit Runge–Kutta methods with some geometric properties. Specially, we provide Runge–Kutta methods with continuous stage which are (conjugate) symplectic, symmetric or energy-preserving for solving Hamiltonian systems. We also present some numerical experiments to verify our results.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.02.042