BDF-α : A Multistep Method with Numerical Damping Control

Abstract

When solving numerically the stiff second order ODE system obtained after semidiscretizing the wave-type partial differential equation (PDE) with the finite element method (FEM), and similarly to the HHT-α method, which allows the numerical damping of the undesirable high frequency modes associated to FEM semidiscretization, we have constructed a modification of the 2-order BDF method (the BDF2 method), which we have called BDF-α. This new method is second-order accurate and with a smaller local truncation error than the BDF2, it is unconditionally stable for some values of α and it permits a parametric control of numerical dissipation.