Linearly-Fitted Conservative (Dissipative) Schemes for Nonlinear Wave Equations

Xinyuan Wu () and Bin Wang ()
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Xinyuan Wu: Nanjing University, Department of Mathematics
Bin Wang: Xi’an Jiaotong University, School of Mathematics and Statistics

Chapter Chapter 8 in Geometric Integrators for Differential Equations with Highly Oscillatory Solutions, 2021, pp 235-261 from Springer

Abstract: Abstract The discrete gradient method is a well-known scheme for the numerical integration of dynamic systems. Its extension to highly oscillatory Hamiltonian systems is called extended discrete gradient method. In this chapter, on the basis of the extended discrete gradient method, we present an efficient approach to devising a structure-preserving scheme for numerically solving conservative (dissipative) nonlinear wave equations. This scheme can preserve the energy exactly for conservative wave equations. With a minor improvement to the extended discrete gradient method, this scheme is applicable to dissipative wave equations, and can preserve the dissipation structure of the underlying dissipative wave equation.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-16-0147-7_8

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DOI: 10.1007/978-981-16-0147-7_8

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