We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution of the problem. In addition, we obtain a monotone sequence of approximate solutions converging uniformly to the solution of the problem, possessing the rate of...

In practice in finite-element stress analysis, the engineer first needs to know if key stresses are converging, and second if they have converged to a reasonable level of accuracy. Then these stresses can be reliably used in design. The engineer further needs to know if, instead, key stresses are diverging because of singularities present. Then these stresses can be of no direct use in design. ...

Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of attraction of the unforced system, must also converge to the equilibrium. This “well-known” but hard-to-cite fact is proved and slightly generalized here.

Supersonic separators have found extensive applications in dehumidification of natural gases since 2003. Unlike previous studies, which have investigated the inlet conditions and nozzle geometry of supersonic separators for pure fluids, the present study employed a combination of momentum, heat, and mass transfer equations along with Virial equation of state (EOS) to inspect the effect of inlet...

Formation of interstellar clouds as a consequence of thermal instability is studied using twodimensional two-fluid magnetohydrodynamic simulations. We consider the situation of converging, supersonic flows of warm neutral medium in the interstellar medium that generate a shocked slab of thermally unstable gas in which clouds form. We found, as speculated in paper I, that in the shocked slab mag...

This work introduces a notion of random dynamical systems with inputs, providing several basic definitions and results on equilibria and convergence. It also presents a “converging input to converging state” (“CICS”) result, a concept that plays a key role in the analysis of stability of feedback interconnections, for monotone systems.

It is shown that for any positive integer n and any function in Lp([0, 1]) with p ∈ [1,∞) there exists a best approximation by linear combinations of n characteristic functions of half-spaces. Further, sequences of such linear combinations converging in distance to the best approximation distance have subsequences converging to the best approximation, i.e., these linear combinations are an appr...

The convergence of nanotechnology, modern biology, the digital revolution and cognitive sciences will bring about tremendous improvements in transformative tools, generate new products and services, enable opportunities to meet and enhance human potential and social achievements, and in time reshape societal relationships. This paper focuses on the progress made in governance of such converging...

in this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (dtm). this is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. several numerical examples are given and by comparing the numerical results obtained from dtm  and  predi...