Two novel classes of energy-preserving numerical approximations for the sine-Gordon equation with Neumann boundary conditions

04/23/2020
by   Qi Hong, et al.
0

We develop two novel classes of energy-preserving algorithms for the sine-Gordon (SG) equation subject to Neumann boundary conditions. The cosine pseudo-spectral method is first employed for spatial discretization under two different meshes to obtain two structure-preserving semi-discrete schemes, which are recast into a finite-dimensional Hamiltonian system and thus admit an energy conservation law. Then we combine a prediction-correction Crank-Nicolson method with an energy projection technique to arrive at fully discrete energy-preserving schemes. Alternatively, we introduce a supplementary variable to transform the SG model into a relaxation system, which is named the supplementary variable method (SVM). Furthermore, we apply the cosine pseudo-spectral method in space and the prediction-correction Crank-Nicolson scheme in time to derive a new class of energy-preserving schemes. The proposed methods can be solved effectively by the discrete Cosine transform. Some benchmark examples are presented to demonstrate the accuracy and efficiency of the proposed schemes. Detailed numerical comparisons among these methods themselves and other reported ones are carried out as well.

READ FULL TEXT
research
06/18/2019

Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation

In this paper, we develop a novel class of arbitrarily high-order energy...
research
11/17/2020

Arbitrary high-order linearly implicit energy-preserving algorithms for Hamiltonian PDEs

In this paper, we present a novel strategy to systematically construct l...
research
09/18/2022

Integrable discretizations of the SIR model

Structure-preserving discretizations of the SIR model are presented by f...
research
05/20/2022

Arbitrary high-order structure-preserving schemes for the generalized Rosenau-type equation

In this paper, we are concerned with arbitrarily high-order momentum-pre...
research
11/25/2019

Structure-preserving algorithms for multi-dimensional fractional Klein-Gordon-Schrödinger equation

This paper aims to construct structure-preserving numerical schemes for ...

Please sign up or login with your details

Forgot password? Click here to reset