An Energy-Preserving and Symmetric Scheme for Nonlinear Hamiltonian Wave Equations

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

Chapter Chapter 10 in Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, 2018, pp 251-268 from Springer

Abstract: Abstract In this chapter, we derive and analyse an energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations, which can exactly preserve the energy of the underlying Hamiltonian wave equations. To this end, we first define and discuss the bounded operator-argument functions on the underlying domain. We then introduce an operator-variation-of-constants formula, based on which we present an energy-preserving scheme for nonlinear Hamiltonian wave equations. The scheme preserves the energy of the original continuous Hamiltonian system exactly. In comparison with the existing work on this topic, such as the well-known Average Vector Field (AVF) formula for Hamiltonian ordinary differential equations, the energy-preserving scheme avoids the semi-discretisation of spatial derivatives and exactly preserves the Hamiltonian of the original continuous Hamiltonian wave equation. This point is very significant in comparison with the AVF formula, since the AVF formula can preserve only the energy of Hamiltonian ordinary differential equations. Hence, the main theme of this chapter is to establish a scheme which can exactly preserve the energy of the nonlinear Hamiltonian wave equation. The chapter is also accompanied by some examples.

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-9004-2_10

Ordering information: This item can be ordered from
http://www.springer.com/9789811090042

DOI: 10.1007/978-981-10-9004-2_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().