Όνομα Περιοδικού:Numerical Methods for Partial Differential Equations
We study the numerical treatment of Boussinesq PDE equation using the method of lines. For the space discretization, we choose either classical finite differences or Fourier pseudospectral methods. Both cases result in a system of second-order ordinary differential equations (ODEs) that is quadratic. In order to take advantage of this special feature, we choose to solve the ODE system using a new type of hybrid Numerov method specially constructed for such problems. Other efficient ODE solvers taken from the literature are used to solve the system of ODEs as well. By taking all the combinations of space discretization methods and ODE solvers, we discuss the stability and accuracy features revealed from the numerical tests.