The Finite Difference Schemes For Two-Dimensional Wave Equations With Neumann Damped Boundary Conditions

In the research field of distributed parameter control systems,the study of the stabi-lization control of the damping boundary wave equation initial boundary value problem is an important research content.Its use value is infiltrated into all aspects of actual produc-tion and life.The analytical solution of the damped wave equation is often very difficult to obtain,and thus hinders the maximum use of its use value.Therefore,we have a numerical algorithm for the two-dimensional wave equation with Neumann damping boundary con-ditions.The research is very important both theoretically and practically.In this thesis,we study the difference scheme of the 2-D wave equation with Neumann damped boundary.First,this thesis deals with the initial-boundary value problem for damped two-dimensional wave equations with Neumann boundaries.a full-discrete is obtained to obtain a three-layer full-discrete implicit finite difference scheme.The prior formula of the constructed difference scheme is proved by the Gronwall inequal-ity,which proves that the established difference scheme is second-order convergent with respect to time and space in the sense of the L2 norm.The solution to the difference scheme is unique and the difference scheme related to the right end term and the initial condition is unconditionally stable.The theoretical results were finally verified by numerical experi-ments.Second,this thesis will use the alternating direction method to establish the above-mentioned alternating direction implicit scheme(ADI scheme),compared with the calcu-lation of the first difference scheme,this scheme calculation is significantly smaller and unconditional stability.For the ADI scheme,by the Gronwall inequality and the discrete energy method,the priori formula is proved.In L2 norm,the established difference scheme is the 1.5 order convergence with respect to time and the established difference scheme is the one convergence with respect to space.The theoretical results were finally verified by numerical experiments.