Error Estimates of Four Level Conservative Finite Difference Schemes for Multidimensional Boussinesq Equation

摘要

A family of four level conservative finite difference schemes (FDS) for the multidimensional Boussinesq Equation is constructed and studied theoretically. A preservation of the discrete energy for this approach is established. We prove that the discrete solution of the FDS converges to the exact solution with a second order of convergence with respect to space and time mesh steps in the first discrete Sobolev norm and in the uniform norm. The numerical experiments for the one-dimensional problem confirm the theoretical rate of convergence and the preservation of the discrete energy in time.