Research On Structure-preserving Algorithms For The Two-dimensional Damped Sine-Gordon Equation

Wang JieComputational MathematicsDirected by Jiang ChaolongStructure-preserving algorithms for the classical nonlinear sine-Gordon equation are well established,however the structure-preserving algorithm of the damped case is still in the early stage.Thus,we devote the present thesis to the construction of structure-preserving algorithms for the two-dimensional damped nonlinear sine-Gordon equation and the main results are listed as follows two aspects.1.Following the ideas of the concatenating method,the original equation is first rewritten as three ordinary differential equations(ODEs),the symplectic midpoint method,the Leap-frog method together with the discrete gradient method are then employed to discretize the three ODEs in time and space respectively,and three conformal multi-symplectic schemes,two local dissipation-energy-preserving schemes and two local momentum-preserving schemes are obtained,respectively.2.Based on the conformal multi-symplectic Hamiltonian system of the original equation,a conformal multi-symplectic Fourier pseudo-spectral scheme is obtained by using the symplectic midpoint method in time as well as the Fourier pseudo-spectral method in space,respectively.