Smoothing \(A\) properties and approximation of time derivatives for parabolic equations: Variable time steps (Q1431669)

A homogeneous parabolic problem is formulated as an abstract initial value problem in Banach space. Smoothing properties and approximation of time derivatives for time-discretization schemes with variable time steps are studied. The time-stepping is based on rational approximations of the exponential function and is \(A(\Theta)\)-stable for suitable \(\Theta\) with unit bounded maximum norm. First- and second-order approximations are treated.