We study the numerical treatment of the Improved Boussinesq PDE equation using the methods 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). We choose to solve the ODE system using a hybrid Numerov method specially constructed for oscillatory problems. In our numerical tests we discuss the stability and accuracy features revealed for one and two soliton solutions.