Symplectic Approximations for Efficiently Solving Semilinear KG 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 11 in Geometric Integrators for Differential Equations with Highly Oscillatory Solutions, 2021, pp 351-391 from Springer

Abstract: Abstract Among typical geometric integrators are multi-symplectic approximations to nonlinear Hamiltonian PDEs. However, it is also an important aspect to analyse the nonlinear stability and convergence when a fully discrete symplectic scheme is designed for nonlinear Hamiltonian PDEs. This chapter presents a symplectic approximation for efficiently solving semilinear Klein–Gordon equations, which can be formulated as an abstract Hamiltonian ordinary differential equation.

Date: 2021
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DOI: 10.1007/978-981-16-0147-7_11

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