1. BDF-α : A Multistep Method with Numerical Damping Control
- Author
-
Juan Jose Anza and Elisabete Alberdi Celaya
- Subjects
Partial differential equation ,Control theory ,Ode ,Applied mathematics ,Dissipation ,Stability (probability) ,Finite element method ,Mathematics::Numerical Analysis ,Parametric statistics ,Mathematics - 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.
- Published
- 2013
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