Convergence of Finite Difference Schemes for a Multidimensional Boussinesq Equation

Conservative finite difference schemes for the numerical solution of multi-dimensional Boussinesq-type equations are constructed and studied theoretically. Depending on the way the nonlinear term f(u) is approximated, two families of finite difference schemes are developed. Error estimates for these numerical methods in the uniform metric and the Sobolev space W21 are obtained. The extensive numerical experiments given in [7] for the one-dimensional problem show good precision and full agreement between the theoretical results and practical evaluation for single soliton and the interaction between two solitons.