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 The variable two-step BDF method for parabolic equations

主讲人：Georgios Akrivis

摘要：The two-step BDF method on variable grids for parabolic equations with self-adjoint elliptic part is considered. Standard stability estimates  for adjacent time-step ratios $r_j:=k_j/k_{j-1}\leqslant 1.8685$ and $1.9104$,  respectively,   have been proved by Becker (1998) and Emmrich (2005) by the energy technique with  a single multiplier. Even slightly improving the ratio is cumbersome. Here,  we  present  a novel technique to examine the positive definiteness of banded matrices that are neither Toeplitz nor weakly diagonally dominant; this result can be viewed as a variant of  the Grenander--Szeg\H{o} theorem. Then, utilizing the energy technique with two multipliers, we establish stability  for adjacent time-step  ratios up to $1.9398$.

主讲人简介：Georgios Akrivis，希腊约阿尼拉大学教授，SIAM J Num. Anal 编委。计算数学顶级专家，主要研究微分方程数值解。在Numer Math, Math Comput, SIAM. J. Numer. Anal等杂志发表SCI论文70余篇。

邀请人：李东方

时间：2024年4月2日（星期二）10:00-12:00

地点：科技楼706室