Abstract
In this chapter we shall first consider approximations at equidistant time levels of parabolic equations in which the time derivate is replaced by a multistep backward difference quotient of maximum order consistent with the number of time steps involved. We show that when this order is at most 6, then the method is stable and has a smoothing property analogous to that of single step methods of type IV. We shall use these properties to derive both smooth and nonsmooth data error estimates. In the end of the chapter we shall also discuss the use of two-step backward difference operators with variable time steps.
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© 1997 Springer-Verlag Berlin Heidelberg
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Thomée, V. (1997). Multistep Backward Difference Methods. In: Galerkin Finite Element Methods for Parabolic Problems. Springer Series in Computational Mathematics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03359-3_10
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DOI: https://doi.org/10.1007/978-3-662-03359-3_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03361-6
Online ISBN: 978-3-662-03359-3
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