On the stability and error structure of BDF schemes applied to linear parabolic evolution equations
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We continue the work of various authors on the stability and error structure of multistep schemes applied to linear evolution equations. BDF schemes are considered, and, as far as reasonable, explicit expressions for all occurring bounds are specified, exploiting prior work on the location of characteristic roots. The 2-step BDF scheme is considered in particular detail, and for problems of sectorial type, an asymptotic error expansion is derived based on damping properties of the scheme.
KeywordsBDF schemes Sectorial operator Stability Asymptotic error expansion
Mathematics Subject Classification (2000)65L06 65M12 65M20 35K90
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