The Finite Difference Schemes For Wave Equation With Robin Damped Boundary Conditions

Stabilization control of the wave equation is an important research content of distributed parameter control theory,the control equation is often wave equation initial and boundary(IBV)problem with feedback boundary conditions.The IBV problem of wave equation with Robin damped boundary is one of them.The research on its numerical algorithm has important theoretical significance and application value.Firstly,this paper is devoted to construct the three level implicit finite difference scheme for the following wave equation with Robin damped boundary and initial conditions.(?)The scheme is a tridiagonal system of linear algebraic equations at each time layer.It is shown that the difference scheme is convergent in maximum norm by discretized energy method and the rate of convergence is of order 2.In addition,the scheme is unconditional stable with respect to initial conditions and right-hand side source term.The numerical experiment verifies the theoretical results.Next,IBV problem(3)is changed to the following equivalent weak coupled hyperbolic equations by introducing a new intermediate variable.(?)Then a novel finite difference scheme of IBV problem(3)is obtained in the manner of constructing full discrete implicit finite difference scheme of(4),therefore the difficulties caused by complex boundary conditions in the IBV problem(3)are avoided.The energy method is adopted to prove that the proposed difference scheme is unconditionally stable with respect to initial conditions and is of two-order convergence in L2 norm.Numerical experiment verifies the theoretical results.Finally,a fully discrete compact finite difference scheme is contructed for wave equation IBV problem(3)with Robin damped boundary.It is certified that it is of four-order convergence about space and two-order convergnce about time in maximum norm by numerical experiment.