Universal Journal of Computational Mathematics(CEASE PUBLICATION) Vol. 1(3), pp. 96 - 108
DOI: 10.13189/ujcmj.2013.010305
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BDF-α : A Multistep Method with Numerical Damping Control

Elisabete Alberdi Celaya^1,*, Juan Jose Anza^2
1 Department of Applied Mathematics, EUIT de Minas y Obras Publicas, Universidad del Pais Vasco UPV/EHU, Bilbao, 48013, Spain
² Department of Applied Mathematics, ETS de Ingenieria de Bilbao, Universidad del Pais Vasco UPV/EHU, Bilbao, 48013, Spain

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.

KEYWORDS
BDF, numerical dissipation, amplification matrix, stability

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Elisabete Alberdi Celaya , Juan Jose Anza , "BDF-α : A Multistep Method with Numerical Damping Control," Universal Journal of Computational Mathematics(CEASE PUBLICATION), Vol. 1, No. 3, pp. 96 - 108, 2013. DOI: 10.13189/ujcmj.2013.010305.

(b). APA Format:
Elisabete Alberdi Celaya , Juan Jose Anza (2013). BDF-α : A Multistep Method with Numerical Damping Control. Universal Journal of Computational Mathematics(CEASE PUBLICATION), 1(3), 96 - 108. DOI: 10.13189/ujcmj.2013.010305.