In this research project our aim is to investigate the convergence of ADI schemes in the numerical solution of multi-dimensional time-dependent PDEs arising in financial mathematics. As mentioned above, these PDEs possess essentially different features from those in other application areas. In particular, mixed spatial derivative terms are pervasive in finance and ADI schemes were not originally developed for PDEs with such terms.
Recently, however, various natural adaptations, of increasing sophistication, have been defined: the Douglas (Do) scheme, the Craig-Sneyd (CS) scheme, the Modified Craig-Sneyd (MCS) scheme and the Hundsdorfer-Verwer (HV) scheme, see [3,11,12,16]. ADI schemes now constitute a main class of numerical methods in academic and industrial finance, and their
range of financial applications continues to extend.