Error Estimates of Four Level Conservative Finite Difference Schemes for Multidimensional Boussinesq Equation
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.
KeywordsSolitary Wave Time Level Finite Difference Scheme Discrete Solution Discrete Energy
This work is partially supported by the Bulgarian Science Fund under grant DDVU 02/71.
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