A theoretical framework for proposed \weak Tau" type of approximation schemes is considered in the context of least-squares parameter estimation problems for partial dierential equations. A convergence theory which includes parameter estimate convergence and method stability is developed. Numerical results demonstrating the possible advantages of these ideas are also presented.

The purpose of this study is to demonstrate the potential of Imperialist CompetitiveAlgorithm (ICA) for solving Blasius dierential equation. This algorithm is inspiredby competition mechanism among Imperialists and colonies and has demonstrated excellentcapabilities such as simplicity, accuracy, faster convergence and better global optimumachievement in contrast to other evolutionary algorithms...

this paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable hilbert space. themain technique is based upon an appropriate composition theorem combined with the banachcontraction mapping principle and an analytic semigroup of linear operators.