Convergence analysis and application of ADI schemes for partial differential equations from financial mathematics.

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 theirrange of financial applications continues to extend.

Keywords:NUMERICAL METHODS

Disciplines:Partial differential equations, Game theory, economics, social and behavioural sciences, Numerical analysis, Numerical computation