Time discretisation of parabolic problems with the variable 3-step BDF
The authors consider the stability of 3-step backward differentiation formula (BDF) on variable grids for the numerical integration of time-dependent parabolic equations. A stability inequality with a stability constant depending in a controllable way on the mesh is obtained. In particular if the ratios \(r_j\) of adjacent mesh-sizes of the underling grid satisfy the bound \(r_j \leq \bar r < 1.199\) than any mixture of the \(j\)-step BDF for \(j=1,2,3\) is stable. From the stability inequality error estimates can be obtained.
scientific article; zbMATH DE number 1876907