Continuous-Stage Leap-Frog Schemes for Semilinear Hamiltonian 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 12 in Geometric Integrators for Differential Equations with Highly Oscillatory Solutions, 2021, pp 393-426 from Springer

Abstract: Abstract The standard leap-frog scheme is a well-known time integration scheme for some nonlinear partial differential equations due to its simplicity and its ease of implementation. The main aim of this chapter is to present continuous-stage modified leap-frog schemes for high-dimensional semilinear Hamiltonian wave equations. We begin with the formulation of the wave equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula.

Date: 2021
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DOI: 10.1007/978-981-16-0147-7_12

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