Efficiency energy-preserving cosine pseudo-spectral algorithms for the sine-Gordon equation with Neumann boundary conditions. Issue 12 (2nd December 2022) - Yue, Xiaopeng; Fu, Yayun
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.