On the Regularization and Stabilization of Approximation Schemes for C 0-Semigroups
Simone Flory, Frank Neubrander, Yu Zhuang · Birkhäuser Basel eBooks · 2001
Many temporal discretization methods for linear evolution equations converge uniformly on compact time intervals at the rate $$\tfrac{1}{{{{n}^{\alpha }}}} $$ only for sufficiently smooth initial data. It is shown that these methods can be regularized such that the new schemes converge ‘in the average’ at the rate $$\tfrac{1} {{n^a }} $$ for all initial data. Examples given include the Crank-Nicholson scheme and the alternating direction implicit method.