Efficiency energy-preserving cosine pseudo-spectral algorithms for the sine-Gordon equation with Neumann boundary conditions

ABSTRACT

This paper considers the newly introduced generalized scalar auxiliary variable approaches to construct high-efficiency energy-preserving schemes for the sine-Gordon equation with Neumann boundary conditions. The equation is first reformulated into an equivalent system by defining a new auxiliary variable that is not limited to square root. Then, the cosine pseudo-spectral method is applied to the system and derive a semi-discrete conservative scheme. Subsequently, we combine the auxiliary variable with the nonlinear term and use an explicit technique discretization in time to derive a fully-discrete energy-preserving scheme. Furthermore, a fast algorithm based on the discrete cosine transform technique reduces the computational complexity in practical computation. Finally, various numerical experiments are displayed to verify the accuracy, efficiency and conservation of the proposed schemes.

KEYWORDS:

• Structure-preserving algorithms
• generalized scalar auxiliary
• sine-Gordon equation
• cosine pseudo-spectral method
• Neumann boundary

AMS SUBJECT CLASSIFICATIONS:

• 65L05
• 65M70

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant Number 11971416). National Natural Science Foundation of Henan Province (Grant Number 222300420280), the National Natural Science Cultivation Foundation of Xuchang University (Grant Number 2022GJPY003), the Scientific Research Projects of Yunnan Education Department (Grant Number 2022J0907).