Symplectic Exponential Runge–Kutta Methods for Solving Nonlinear Hamiltonian Systems

Xinyuan Wu () and Bin Wang
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Xinyuan Wu: Nanjing University, Department of Mathematics
Bin Wang: Qufu Normal University, School of Mathematical Sciences

Chapter Chapter 4 in Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, 2018, pp 85-106 from Springer

Abstract: Abstract Symplecticity is an important property for exponential Runge–Kutta (ERK) methodsERK methods when the underlying problem $$y'(t)=My(t)+f(y(t))$$ is a Hamiltonian system. The main theme of this chapter is to present symplectic exponential Runge–Kutta methods. UsingSymplectic exponential Runge–Kutta methods Nonlinear Hamiltonian systems the fundamental analysis of geometric integrators, we first derive and analyse the symplectic conditions for ERK methods. These conditions reduce to the conventional ones when $$M\rightarrow \mathbf {0}$$ . Furthermore, revised stiff order conditions are proposed and investigated in detail. This chapter is also accompanied by numerical results that demonstrate the potential of the symplectic ERK methods.

Keywords: Exponential Runge Kutta (ERK); ERK Methods; Hamiltonian Systems; Symplectic Condition; Stiff Order (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-9004-2_4

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DOI: 10.1007/978-981-10-9004-2_4

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