Structure-Preserving Exponential Runge-Kutta Methods

Keywords

Conformal symplectic; Exponential integrators; Exponential time differencing; Integrating factor methods; Structure-preserving algorithm; Time-dependent damping

Abstract

Exponential Runge-Kutta (ERK) and partitioned exponential Runge-Kutta (PERK) methods are developed for solving initial value problems with vector fields that can be split into conservative and linear nonconservative parts. The focus is on linearly damped ordinary differential equations that possess certain invariants when the damping coefficient is zero, but, in the presence of constant or time-dependent linear damping, the invariants satisfy linear differential equations. Similar to the way that Runge-Kutta and partitioned Runge-Kutta methods preserve quadratic invariants and symplecticity for Hamiltonian systems, ERK and PERK methods exactly preserve conformal symplecticity, as well as decay (or growth) rates in linear and quadratic invariants, under certain constraints on their coefficient functions. Numerical experiments illustrate the higher-order accuracy and structure-preserving properties of various ERK methods, demonstrating clear advantages over classical conservative Runge-Kutta methods, as well as usefulness for solving a wide range of differential equations.

Publication Date

1-1-2017

Publication Title

SIAM Journal on Scientific Computing

Volume

39

Issue

2

Number of Pages

A593-A612

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/16M1071171

Socpus ID

85018289494 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85018289494

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