Numerical experiments of some Krylov subspace methods for black oil model

This paper discusses preconditioned Krylov subspace methods for solving large scale linear systems that originate from oil reservoir numerical simulations. Two types of preconditioners, one being based on an incomplete LU decomposition and the other being based on iterative algorithms, are used together in a combination strategy in order to achieve an adaptive and efficient preconditioner. Numerical tests show that different Krylov subspace methods combining with appropriate preconditioners are able to achieve optimal performance.

On a parallel time-domain method for the nonlinear Black-Scholes equation

A parallel time-domain algorithm is described for the time-dependent nonlinear Black-Scholes equation, which may be used to build financial analysis tools to help traders making rapid and systematic evaluation of buy/sell contracts. The algorithm is particularly suitable for problems that do not require fine details at each intermediate time step, and hence the method applies well for the present problem.

Constructive trusts, illegal purpose and locus poenitentiae

Analyses the Family Division decision in Q v Q on the competing claims of a father and son to beneficial ownership of a house in which the father sought to on a secret agreement entered into with his sons when transferring the property into their joint names, intended to subvert the inheritance tax rules on lifetime gifts by retaining the right to have the property transferred back to him, and the son relied on a later agreement with his brother to transfer the house into his sole name, in reliance on which he and his wife had acted to their detriment by paying for its upkeep and renovation.