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Partial differentials

S = Moreover, because the order of partial differentiation is innnaterial, one obtains as cross-... [Pg.348]

The solutions of such partial differential equations require infomiation on the spatial boundary conditions and initial conditions. Suppose we have an infinite system in which the concentration flucPiations vanish at the infinite boundary. If, at t = 0 we have a flucPiation at origin 5C(f,0) = AC (f), then the diflfiision equation... [Pg.721]

Doolen G D (ed.) 1990 Lattice Gas Methods for Partial Differential Equations (Redwood City, CA Addison-Wesley)... [Pg.2387]

In this paper, we discuss semi-implicit/implicit integration methods for highly oscillatory Hamiltonian systems. Such systems arise, for example, in molecular dynamics [1] and in the finite dimensional truncation of Hamiltonian partial differential equations. Classical discretization methods, such as the Verlet method [19], require step-sizes k smaller than the period e of the fast oscillations. Then these methods find pointwise accurate approximate solutions. But the time-step restriction implies an enormous computational burden. Furthermore, in many cases the high-frequency responses are of little or no interest. Consequently, various researchers have considered the use of scini-implicit/implicit methods, e.g. [6, 11, 9, 16, 18, 12, 13, 8, 17, 3]. [Pg.281]

It is only for smooth field models, in this sense, that partial differential equations relating species concentrations to position in space can be written down. However, a pore geometry which is consistent with the smooth... [Pg.64]

Regarded as an equation for e, this is a member of the class of elliptic partial differential equations for which a maximum principle is satisfied [76], SO e is required to take its greatest and least values on the... [Pg.147]

Equations (12,13) and (12,14) together then provide (n+ 1) partial differential equations in the unknowns c, T. They may be solved subject Co boundary conditions specified at the pellet surface at all times, and Initial conditions specified throughout the interior of the pellet at one particular time. [Pg.162]

Equations (12.29) - (12.31) provide three partial differential equations in three unknowns p and T (since = 1-x ). The boundary condi-... [Pg.167]

On subsciCuLlng (12.49) into uhe dynamical equations we may expand each term in powers of the perturbations and retain only terms of the zeroth and first orders. The terms of order zero can then be eliminated by subtracting the steady state equations, and what remains is a set of linear partial differential equations in the perturbations. Thus equations (12.46) and (12.47) yield the following pair of linearized perturbation equations... [Pg.172]

Development of weighted residual finite element schemes that can yield stable solutions for hyperbolic partial differential equations has been the subject of a considerable amount of research. The most successful outcome of these attempts is the development of the streamline upwinding technique by Brooks and Hughes (1982). The basic concept in the streamline upwinding is to modify the weighting function in the Galerkin scheme as... [Pg.54]

Consider a partial differential equation, representing a time dependent flow problem given as... [Pg.66]

Lapidus, L. and Pinder, G. F., 1982. Numerical Solution of Partial Differential Equations in Science and Engineering, Wiley, New York. [Pg.68]

Mitchell, A.R. and Wait, R., 1977. The Finite Element Method in Partial Differential Ecjualions, Wiley, London. [Pg.68]

Differential methods - in these techniques the internal grid coordinates are found via the solution of appropriate elliptic, parabolic or hyperbolic partial differential equations. [Pg.195]

Kondrat ev V.A., Oleinik O.A. (1983) Boundary value problems for partial differential equations in nonsmooth domains. Uspekhi Mat. Nauk 38 (2), 3-76 (in Russian). [Pg.380]

Mikhailov V.P. (1976) Partial differential equations. Nauka, Moscow (in Russian). [Pg.382]

Yakunina G.V. (1981) Smoothness of solutions of variational inequalities. Partial differential equations. Spectral theory. Leningrad Univ. (8), 213-220 (in Russian). [Pg.386]

Dyna.micPerforma.nce, Most models do not attempt to separate the equiUbrium behavior from the mass-transfer behavior. Rather they treat adsorption as one dynamic process with an overall dynamic response of the adsorbent bed to the feed stream. Although numerical solutions can be attempted for the rigorous partial differential equations, simplifying assumptions are often made to yield more manageable calculating techniques. [Pg.286]

These models are usually categorized according to the number of supplementary partial differential transport equations which must be solved to supply the modeling parameters. The so-called zero-equation models do not use any differential equation to describe the turbulent quantities. The best known example is the Prandtl (19) mixing length hypothesis ... [Pg.102]

Dynamic meteorological models, much like air pollution models, strive to describe the physics and thermodynamics of atmospheric motions as accurately as is feasible. Besides being used in conjunction with air quaHty models, they ate also used for weather forecasting. Like air quaHty models, dynamic meteorological models solve a set of partial differential equations (also called primitive equations). This set of equations, which ate fundamental to the fluid mechanics of the atmosphere, ate referred to as the Navier-Stokes equations, and describe the conservation of mass and momentum. They ate combined with equations describing energy conservation and thermodynamics in a moving fluid (72) ... [Pg.383]

Mathematical and Computational Implementation. Solution of the complex systems of partial differential equations governing both the evolution of pollutant concentrations and meteorological variables, eg, winds, requires specialized mathematical techniques. Comparing the two sets of equations governing pollutant dynamics (eq. 5) and meteorology (eqs. 12—14) shows that in both cases they can be put in the form ... [Pg.384]

Consider the crystallizer shown in Figure 11. If it is assumed that the crystallizer is well mixed with a constant slurry volume FTp then, as shown (7), the following partial differential population balance can be derived ... [Pg.348]

Smith, I. M., J. L. Siemienivich, and I. Gladweh. A Comparison of Old and New Methods for Large Systems of Ordinary Differential Equations Arising from Parabolic Partial Differential Equations, Num. Anal. Rep. Department of Engineering, no. 13, University of Manchester, England (1975). [Pg.424]

Vemuri, V, and W. Karplus. Digital Computer Treatment of Partial Differential Equations. Prentice Hall, Englewood Cliffs, NJ (1981). [Pg.424]

The description of phenomena in a continuous medium such as a gas or a fluid often leads to partial differential equations. In particular, phenomena of wave propagation are described by a class of partial differential equations called hyperbolic, and these are essentially different in their properties from other classes such as those that describe equilibrium ( elhptic ) or diffusion and heat transfer ( para-bohc ). Prototypes are ... [Pg.425]

Partial Derivative The abbreviation z =f x, y) means that is a function of the two variables x and y. The derivative of z with respect to X, treating y as a constant, is called the partial derivative with respecd to x and is usually denoted as dz/dx or of x, y)/dx or simply/. Partial differentiation, hke full differentiation, is quite simple to apply. Conversely, the solution of partial differential equations is appreciably more difficult than that of differential equations. [Pg.443]


See other pages where Partial differentials is mentioned: [Pg.498]    [Pg.739]    [Pg.741]    [Pg.193]    [Pg.212]    [Pg.281]    [Pg.111]    [Pg.114]    [Pg.141]    [Pg.156]    [Pg.159]    [Pg.47]    [Pg.17]    [Pg.18]    [Pg.54]    [Pg.54]    [Pg.102]    [Pg.153]    [Pg.101]    [Pg.101]    [Pg.384]    [Pg.97]    [Pg.420]    [Pg.420]   
See also in sourсe #XX -- [ Pg.92 , Pg.104 ]

See also in sourсe #XX -- [ Pg.70 ]




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Applications of Partial Differential Equations in Chemical Engineering

Calculus of Partial Differentials

Chemical engineering partial differential equations

Classification of Partial Differential Equations

Condensation, differential partial

Condensation, differential partial fractional

Contrast structures partial differential equations

Coupled partial differential equations

Cystic partially differentiated nephroblastoma

Difference formulae for partial differential

Difference formulae for partial differential equations

Differentiability partial

Differential calculus partial

Differential coefficient partial

Differential equations partial

Differential equations, partial derivation

Differential partially structured systems

Distributed systems partial differential equations

Equations, adjoint partial differential

Finite difference method partial differential equation

Finite element method partial differential equation

First order hyperbolic partial differential

First order hyperbolic partial differential equations

First order parabolic partial differential

First order parabolic partial differential equation

Gauss-Newton Method for Partial Differential Equation (PDE) Models

Hamiltonian function partial differential equation

Laplace Transform Technique for Partial Differential Equations (PDEs) in Finite Domains

Laplace transform technique for partial differential equations

Laplace transform technique partial differential equations

Laws partial differential equations

Laws partial differential-algebraic equation

Linear Parabolic Partial Differential Equations

Linear partial differential equations

Mathematical methods partial differential equations

Method of Lines for Elliptic Partial Differential Equations

Method of lines for parabolic partial differential equations

Nonlinear Parabolic Partial Differential Equations

Numerical Method of Lines for Parabolic Partial Differential Equations (PDEs)

Numerical Methods for Solution of Partial Differential Equations

Numerical Solution of Partial Differential Equations

Numerical analysis partial differential equations

Numerical computational methods partial differential equations

Numerical methods partial differential equations

Oscillation Model partial differential equation

Partial Derivatives and Total Differentials

Partial Differential Equation systems elliptic equations

Partial Differential Equation systems hyperbolic equations

Partial Differential Equation systems parabolic equations

Partial Differential Equations (PDEs) in Semi-infinite Domains

Partial Differential Equations Waves in a String

Partial Differential Equations and Special Functions

Partial Differential Equations in Finite Domains

Partial Differential Equations in Semi-infinite Domains

Partial Differential Equations in Time and One Space Dimension

Partial Differential Equations in Two Space Dimensions

Partial Differential Equations of Voltages and Currents

Partial Differential Relationships

Partial differential across

Partial differential across control

Partial differential cross section

Partial differential cross section product state distributions

Partial differential equation (PDE) method

Partial differential equation characteristic values

Partial differential equation conditional stability

Partial differential equation eigenfunctions

Partial differential equation eigenvalues

Partial differential equation elliptic

Partial differential equation finite differences

Partial differential equation first-order linear

Partial differential equation higher orders

Partial differential equation homogeneous

Partial differential equation hydrogen atom

Partial differential equation hyperbolic

Partial differential equation medium

Partial differential equation nonhomogeneous

Partial differential equation nonlinear

Partial differential equation numerical approximation methods

Partial differential equation order

Partial differential equation parabolic

Partial differential equation quasi linear

Partial differential equation second-order linear

Partial differential equation similarity transformations

Partial differential equation stability

Partial differential equation unstability

Partial differential equations 22 INDEX

Partial differential equations Fourier transform

Partial differential equations Laplace transform

Partial differential equations Sturm-Liouville equation

Partial differential equations asymptotic solutions

Partial differential equations boundary conditions

Partial differential equations characteristics with reaction

Partial differential equations computational fluid mechanics

Partial differential equations computer software

Partial differential equations diffusion modeling

Partial differential equations dimensions

Partial differential equations finite volume methods

Partial differential equations first order

Partial differential equations formulation

Partial differential equations frequency domain

Partial differential equations heat conduction problem

Partial differential equations inhomogeneous

Partial differential equations initial value type

Partial differential equations linear second-order hyperbolic

Partial differential equations local coordinates

Partial differential equations model

Partial differential equations nondimensionalization

Partial differential equations numerical solution

Partial differential equations orthogonal function

Partial differential equations overview

Partial differential equations particular solution

Partial differential equations processes governed

Partial differential equations setting

Partial differential equations similarity solutions

Partial differential equations simple waves

Partial differential equations standard Laplace transforms

Partial differential equations steady-state heat transfer

Partial differential equations systems

Partial differential equations temperature

Partial differential equations the finite differences method

Partial differential equations time derivative

Partial differential equations unsteady heat transfer

Partial differential equations, Laplace

Partial differential equations, Yang-Mills

Partial differential equations, numerical

Partial differential equations, step-type contrast solutions

Partial differential operators

Partial differential-algebraic equation

Partial differential-algebraic equation PDAE)

Partial differentiation

Partial differentiation changing independent variables

Partial least square differential analysis

Partial retention of diatomic differential

Partial retention of diatomic differential overlap

Quasilinear partial differential equation

Reduction to a single partial differential equation

Scattering cross section partial differential

Second order hyperbolic partial differential equations

Second order partial differential equation

Second-order linear partial differential

Second-order partial differential

Second-order partial differential equations and Greens functions

Semianalytical Method for Parabolic Partial Differential Equations (PDEs)

Semianalytical method for parabolic partial differential equation

Separation of Variables Method for Partial Differential Equations (PDEs) in Finite Domains

Setting Up Partial Differential Equations

Similarity Solution Technique for Elliptic Partial Differential Equations

Similarity Solution Technique for Nonlinear Partial Differential Equations

Solution of Parabolic Partial Differential Equations for Diffusion

Solution of Parabolic Partial Differential Equations for Heat Transfer

Solution of Partial Differential Equations

Solution of Partial Differential Equations Using Finite Differences

Stiff nonlinear partial differential

Stiff nonlinear partial differential equations

Techniques for the numerical solution of partial differential equations

What is the solution of a partial differential equation

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