| As the basic mathematical model for describing the quantization vortex of superfluid,the partial differential equations with rotation terms have already become one of the key issues concerned by many researchers.In this paper,the finite difference method of two types partial differential equations with rotation terms are analyzed,including the coupled Gross–Pitaevskii equations and Klein-Gordon equation.The main contents of this paper are summarized as fol-lows:Firstly,the finite difference method for coupled Gross–Pitaevskii equations with rotation terms is studied.We construct a linearized difference scheme and a nonlinear Crank-Nicolson scheme respectively,prove that both schemes are uniquely solvable,and inherit the conser-vation laws of mass and energy in the discrete sense.Then,referring to the energy method,mathematical induction,‘cut-off’function technique and some inequalities commonly used in the literature,the optimal error estimates of these algorithms are established in the sense of L~∞-norm without any restrictions on the parameters of discrete grid.The numerical experiments further verified our theoretical analysis.After that,the finite difference method for Klein-Gordon equation with second-order angu-lar momentum rotation terms are studied in this paper.Due to the presence of strong centrifugal forces in the model,inappropriate spatial discretization of the second-order rotation term will lead to numerical instability at the boundary,which cannot be overcome through the averaging technique in the time direction and the conservation property of mass and energy.Through nu-merical experiments,the boundary stable discretizations of the second-order rotation term are determined,and on this basis,several boundary stable finite difference schemes are proposed,including linear and nonlinear,conservative and nonconservative schemes,and the extended schemes with four-order accuracy in spatial direction.Lastly,numerical experiments are pro-vided to verify the accuracy,conservation properties and effectiveness of proposed schemes. |
