Let the parabolic problem c(x, t, u)ut = a(x, t, u)u,. + b(x, t, u, ut), 0 < x < 1, O < t < T, u(x, 0) = f(x), u(O, t) = go(t), u(l, t) = g1(t), be solved approximately by the continuous-time collocation process based on having the differential equation satisfied at

/pdf/a-finite-element-collocation-method-for-quasilinear-2a2jq2j0p0.pdf

First Principles of Numerical Analysis. By Burton Wendroff. 1969. (Addison-Wesley.)

A finite element collocation method for quasilinear parabolic equations

We present an exact theoretical kinetic formalism which specifically treats the temporal evolution of the various chemical functional groups about a specific silicon atom undergoing concurrent hydrolysis and condensation reactions This formalism is applied to the chemical kinetics of a typical sol-gel reaction system We also present a simplified statistical reaction model which reduces the number of chemically distinct rate coefficients necessary to describe the kinetics from 165 to 3 Experimental results which support this statistical model are also presented

Sol−gel kinetics. II: Chemical speciation modeling

Poisson and negative binomial models are applied to the number of multiple victimizations reported in the National Crime Surveys. The negative binomial but not the Poisson models is shown to be com...

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Multiple Victimization in American Cities: A Statistical Analysis of Rare Events

: Sea spray droplets initially have the same temperature as the ocean surface from which they formed. In high latitudes, under a relatively cold wind, they therefore cool and evaporate, in effect enhancing the air-sea exchange of heat and moisture. With a future goal of investigating this enhanced exchange in mind, this report develops model equations with which to track the thermal and size (moisture content) evolution of a spray droplet from the time it is created until it comes to equilibrium with its environment. On testing the model against some of the scanty data available on the evolution of saline droplets, good agreement is found. The ambient humidity has little effect on the thermal exchange, and, analogously, the initial droplet temperature has negligible effect on the moisture exchange.

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Thermal and Size Evolution of Sea Spray Droplets

The stochastic evolution of a well stirred chemically reacting system containing a single time‐varying species X is accurately described by the master equation, in which the total number x of X molecules is an integer variable. We investigate here the legitimacy of approximating the master equation by a Fokker–Planck type partial differential equation in which x is treated as a real variable. Taking the position that any partial differential equation may be regarded as a legitimate approximation to the master equation if and only if it reduces to the master equation when subjected to a proper discretization procedure, we deduce the following: For the special case in which the various chemical reactions can alter the X molecule population by no more than one molecule at a time, a second order (two term) Fokker–Planck equation suffices. However, for the more general case in which reactions are allowed that alter the X molecule population by two molecules at a time, it is necessary to use at least a fourth o...

First Principles of Numerical Analysis. By Burton Wendroff. 1969. (Addison-Wesley.)

Citations

A finite element collocation method for quasilinear parabolic equations

Sol−gel kinetics. II: Chemical speciation modeling

Multiple Victimization in American Cities: A Statistical Analysis of Rare Events

Thermal and Size Evolution of Sea Spray Droplets

Approximating the master equation by Fokker–Planck‐type equations for single‐variable chemical systems

Related Papers (1)

Theoretical Numerical Analysis (Burton Wendroff)