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First order hyperbolic partial differential equations

The model for this crystallizer configuration has been shown to consist of the well known population balance (4), coupled with an ordinary differential equation, the concentration balance, and a set of algebraic equations for the vapour flow rate, the growth and nucleatlon kinetics (4). The population balance is a first-order hyperbolic partial differential equation ... [Pg.160]

Lax-Wendroff. This is a well known method to solve first-order hyperbolic partial differential equations in boundary value problems. The two step Richtmeyer implementation of the explicit Lax-Wendroff differential scheme is used (8). [Pg.164]

Transient heat conduction or mass transfer in solids with constant physical properties (diffusion coefficient, thermal diffusivity, thermal conductivity, etc.) is usually represented by a linear parabolic partial differential equation. In this chapter, we describe how one can arrive at the analytical solutions for linear first order hyperbolic partial differential equations and parabolic partial differential equations in finite domains using the Laplace transform technique. [Pg.679]

Linear first order hyperbolic partial differential equations are solved using Laplace transform techniques in this section. Hyperbolic partial differential equations are first order in the time variable and first order in the spatial variable. The method involves applying Laplace transform in the time variable to convert the partial differential equation to an ordinary differential equation in the Laplace domain. This becomes an initial value problem (IVP) in the spatial direction with s, the Laplace variable, as a parameter. The boundary conditions in x are converted to the Laplace domain and the differential equation in the Laplace domain is solved by using the techniques illustrated in chapter 2.1 for solving linear initial value problems. Once an analytical solution is obtained in the Laplace domain, the solution is inverted to the time domain to obtain the final analytical solution (in time and spatial coordinates). This is best illustrated with the following example. [Pg.679]

Rhee, Aris, and Amundson, First-Order Partial Differential Equations Volume 1. Theory and Application of Single Equations Volume 2. Theory and Application of Hyperbolic Systems of Quasi-Linear Equations, Prentice Hall, Englewood Cliffs, New Jersey, 1986,1989. [Pg.4]

Rhee, H.K., Aris, R., and Amundson, N.R. (1986) First-order partial differential equations, in Theory and Application of Hyperbolic Systems of Quasilinear Equations, vol. I, Prentice-Hall, New Jersey. [Pg.422]


See other pages where First order hyperbolic partial differential equations is mentioned: [Pg.557]    [Pg.749]    [Pg.749]    [Pg.768]    [Pg.343]    [Pg.196]   
See also in sourсe #XX -- [ Pg.678 , Pg.838 , Pg.839 , Pg.848 , Pg.855 , Pg.858 ]




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Differential equations order

Differential equations partial

Differential first-order

Differential order

Equation hyperbolic

Equations first-order

First equation

First order hyperbolic partial differential

First-order differential equation

Hyperbolic

Hyperbolicity

Order equation

Partial Ordering

Partial differential

Partial differential equation order

Partial differential equations first order

Partial equation

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