Discrete maximal regularity of time-stepping schemes for fractional evolution equations (Q1692303)

The authors analyze the regularity of classical time stepping schemes applied to fractional evolution equations with derivative of order \(\alpha\), \(\alpha\in]0,2[\), \(\alpha\neq 1\). More precisely, conditions are derived under which the time discretizations preserve the \(l^p\)-regularity uniformly in the step-size. Analysis is provided i.e. for the backward Euler, the Crank-Nicolson and the BDF 2 method. The main technical tools used are operator-valued Fourier multiplier theorems. Finally, some numerical examples were presented.