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2018 | OriginalPaper | Buchkapitel

9. An Integral Formula Adapted to Different Boundary Conditions for Arbitrarily High-Dimensional Nonlinear Klein–Gordon Equations

verfasst von : Xinyuan Wu, Bin Wang

Erschienen in: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

Verlag: Springer Singapore

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Abstract

This chapter is concerned with the initial-boundary value problem for arbitrarily high-dimensional Klein–Gordon equations, posed on a bounded domain \(\varOmega \subset \mathbb {R}^d\) for \(d \ge 1\) and subject to suitable boundary conditions. We derive and analyse an integral formula which proves to be adapted to different boundary conditions for general Klein–Gordon equations in arbitrarily high-dimensional spaces.

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Vorheriges Kapitel A Compact Tri-Colored Tree Theory for General ERKN Methods

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

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Titel: An Integral Formula Adapted to Different Boundary Conditions for Arbitrarily High-Dimensional Nonlinear Klein–Gordon Equations
verfasst von: Xinyuan Wu
Bin Wang
Verlag: Springer Singapore
Buch: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations
Print ISBN: 978-981-10-9003-5

Electronic ISBN: 978-981-10-9004-2

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-981-10-9004-2_9

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