A Multicomponent Alternating Direction Method for Numerical Solution of Boussinesq Paradigm Equation

We construct and analyze a multicomponent alternating direction method (a vector additive scheme) for the numerical solution of the multidimensional Boussinesq Paradigm Equation (BPE). In contrast to the standard splitting methods at every time level a system of many finite difference schemes is solved. Thus, a vector of the discrete solutions to these schemes is found. It is proved that these discrete solutions converge to the continuous solution in the uniform mesh norm with O(vertical bar h vertical bar(2) + tau) order. The method provides full approximation to BPE and is efficient in implementation. The numerical rate of convergence and the altitudes of the crests of the traveling waves are evaluated.