New conservative schemes with discrete variational derivatives for nonlinear wave equations

Authors:
Takayasu Matsuo
Affiliations:
Interfaculty Initiative in Information Studies, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 8
Cited 8

A Hamiltonian explicit algorithm with spectral accuracy for the `good' Boussinesq system

ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Two energy conserving numerical schemes for the sine-Gordon equation

Applied Mathematics and Computation
Finite difference calculus invariant structure of a class of algorithms for the nonlinear Klein-Gordon equation

SIAM Journal on Numerical Analysis
Finite difference schemes for 6u6t= 66x adGdu that inherit energy conservation or dissipation property

Journal of Computational Physics
Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations

Journal of Computational Physics
Finite-difference schemes for nonlinear wave equation that inherit energy conservation property

Journal of Computational and Applied Mathematics
High-order schemes for conservative or dissipative systems

Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Numerical investigation for the solitary waves interaction of the "good&" Boussinesq equation

Applied Numerical Mathematics

Numerical simulation of a nonlinearly coupled Schrödinger system: A linearly uncoupled finite difference scheme

Mathematics and Computers in Simulation
Analysis of a symplectic difference scheme for a coupled nonlinear Schrödinger system

Journal of Computational and Applied Mathematics
An extension of the discrete variational method to nonuniform grids

Journal of Computational Physics
Conservative numerical schemes for the Ostrovsky equation

Journal of Computational and Applied Mathematics
Interacting Wave Fronts and Rarefaction Waves in a Second Order Model of Nonlinear Thermoviscous Fluids

Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
A General Framework for Deriving Integral Preserving Numerical Methods for PDEs

SIAM Journal on Scientific Computing
The discrete variational derivative method based on discrete differential forms

Journal of Computational Physics
Local structure-preserving algorithms for the "good" Boussinesq equation

Journal of Computational Physics

Quantified Score

Hi-index	7.31

Visualization

Abstract

New conservative finite difference schemes for certain classes of nonlinear wave equations are proposed. The key tool there is ''discrete variational derivative'', by which discrete conservation property is realized. A similar approach for the target equations was recently proposed by Furihata, but in this paper a different approach is explored, where the target equations are first transformed to the equivalent system representations which are more natural forms to see conservation properties. Applications for the nonlinear Klein-Gordon equation and the so-called ''good'' Boussinesq equation are presented. Numerical examples reveal the good performance of the new schemes.