A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach

This paper aims to develop a linearly implicit structure-preserving numerical scheme for the space fractional sine-Gordon equation, which is based on newly developed invariant energy quadratization method. First, we reformulate equation as canonical Hamiltonian system by virtue of variational derivative functional with Laplacian. Then, utilize centered difference formula discrete equivalent derived method in direction, and obtain conservative semi-discrete scheme. Subsequently, applied resulting arrive at fully-discrete The stability, solvability convergence maximum norm are given. Furthermore, fast algorithm Fourier transformation technique used reduce computational complexity practical computation. Finally, examples provided confirm our theoretical analysis results.