A defect equation approach for the coupling of subdomains in domain decomposition methods

A defect equation for the coupling of nonlinear subproblems defined in nonoverlapped subdomains arise in domain decomposition methods is presented. Numerical solutions of defect equations by means of quasi-Newton methods are considered.

An improved result of exponential stability of stochastic semilinear evolution equations

Sufficient conditions for the exponential stability of a class ofnonlinear, non-autonomous stochastic differential equations in infinitedimensions are studied. The analysis consists of introducing a suitableapproximating solution systems and using a limiting argument to pass onstability of strong solutions to mild ones. As a consequence, the classicalcriteriaof stability in A. Ichikawa [8] are improved and extended to cover a class ofnon-autonomous stochastic evolution equations.Two examples are investigated to illustrate our theory.

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.