# Encyclopedia of Applied and Computational Mathematics

2015 Edition
| Editors: Björn Engquist

# Backward Differentiation Formulae

• Jeff R Cash
Reference work entry
DOI: https://doi.org/10.1007/978-3-540-70529-1_94

## Synonyms

Extended backward differentiation formulae; Linear multistep methods

## Definition

Backward differentiation formulae (BDF) are linear multistep methods suitable for solving stiff initial value problems and differential algebraic equations. The extended formulae (MEBDF) have considerably better stability properties than BDF.

## Review of Stiffness

We derive BDF and MEBDF suitable for solving stiff initial value problems and differential algebraic equations. In this section, we will be concerned with a special class of multistep methods for the approximate numerical integration of first-order systems of ordinary differential equations of the form
$$\displaystyle{ \frac{dy} {dx} = f(x,y),\quad y(a) = y_{a}. }$$
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## References

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Cash, J.R.: The integration of stiff initial value problems in ODEs using modified extended backward differentiation formulae. Comput. Math. Appl. 9(5), 645–657 (1983)
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