Thesiss

It has long been known that high frequency components, typically from nonsmooth data, can cause spurious oscillations in numerical schemes. Luskin and Rannacher for the Crank-Nicolson scheme, and Rannacher for diagonal Padé schemes in general, discovered that the use of (m − 1, …

Numerical schemes often develop inaccuracies when used to solve parabolic partial differential equations with nonsinooth data e.g., from high frequency components. For homogeneous parabolic PDEs with nonsinooth data, Luskin and Rannacher [60, 61] discovered for the case of Crank…