ScholarLens Back to search
1994•Unpublished venueRequires access

REDUCIBILITY AND CHARACTERIZATION OF SYMPLECTIC RUNGE{KUTTA METHODS

Rudolf Scherer

Open publisher page 6 citations

Abstract

Dedicated to Professor Wilhelm Niethammer on the occasion of his 60th birthday. Abstract. Hamiltonian systems arise in many areas of physics, mechanics, and engineering sciences as well as in pure and applied mathematics. To their symplectic integration certain Runge{Kutta{ type methods are protably applied (see Sanz{Serna and Calvo (10)). In this paper Runge{Kutta and partitioned Runge{Kutta methods are considered. Dierent features of symmetry are distinguished using reflected and transposed methods. The property of DJ{irreducibility ensures symplectic meth- ods having nonvanishing weights. A characterization of symplectic methods is deduced, from which many attributes of such methods and hints for their construction follow. Order conditions up to order four can be checked easily by simplifying assumptions. For symplectic singly{implicit Runge{Kutta methods the order barrier is shown to be two.

About this research paper

What this paper is about

Dedicated to Professor Wilhelm Niethammer on the occasion of his 60th birthday. Abstract. Hamiltonian systems arise in many areas of physics, mechanics, and engineering sciences as well as in pure and applied mathematics. To their symplectic integration certain Runge{Kutta{ type methods are protably applied (see Sanz{Serna and Calvo (10)). In this paper Runge{Kutta and partitioned Runge{Kutta methods are considered. Dierent features of symmetry are distinguished using reflected and transposed methods. The property of DJ{irreducibility ensures symplectic meth- ods having nonvanishing weights. A characterization of symplectic methods is deduced, from which many attributes of such methods and hints for their construction follow. Order conditions up to order four can be checked easily by simplifying assumptions. For symplectic singly{implicit Runge{Kutta methods the order barrier is shown to be two.

Why it matters

OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Dedicated to Professor Wilhelm Niethammer on the occasion of his 60th birthday. Abstract. Hamiltonian systems arise in many areas of physics, mechanics, and engineering sciences as well as in pure and applied mathematics. To their symplectic integration certain Runge{Kutta{ type methods are protably applied (see Sanz{Serna and Calvo (10)). In this paper Runge{Kutta and partitioned Runge{Kutta methods are considered. Dierent features of symmetry are distinguished using reflected and transposed methods. The property of DJ{irreducibility ensures symplectic meth- ods having nonvanishing weights. A characterization of symplectic methods is deduced, from which many attributes of such methods and hints for their construction follow. Order conditions up to order four can be checked easily by simplifying assumptions. For symplectic singly{implicit Runge{Kutta methods the order barrier is shown to be two.

Key concepts: Symplectic geometry, Runge–Kutta methods, Irreducibility, Mathematics, Symplectic integrator, Applied mathematics, Hamiltonian (control theory), Hamiltonian system

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
REDUCIBILITY AND CHARACTERIZATION OF SYMPLECTIC RUNGE{KUTTA METHODS — Research Paper | ScholarLens