Numerical Study of the Good Boussinesq Equation

Abstract In this paper we evaluate propagating wave solutions to the one-dimensional good Boussinesq Equation (BE). Two numerical methods are used to obtain a solution. The first is a conservative finite difference scheme, and the second exploits Taylor series expansions around the time variable t . The solutions are computed over nested meshes to examine the convergence of both approaches. The main tool for testing the convergence rate of all examined finite difference schemes and Taylor expansions is the Runge’s method. It is shown that for a fixed time interval the numerical methods preserve the shape of the waves after interaction and mass of the solution. The waves obtained by the two methods are compared with the exact solution. Both methods produce similar results in case of O ( h 2 + τ 2 ) approximation order, with errors measured in L 2 and L ∞ norms which are 100 times or less than the solution maximum.