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Useful numerical analysis

The value of the parameter n in Eqs. (9.13)—(9.14) is different from unity, and these differential equations are nonlinear and cannot be solved analytically. Therefore, Eqs. (9.13)-(9.16) subject to the conditions of Eqs. (9.17)-(9.21) were solved using numerical analysis techniques. Selim et al. (1976a) used the explicit-implicit finite-difference approximations as the method of solution. This was successfully used by Selim et al. (1975) for steady water flow conditions and by Selim et al. (1976a) for transient... [Pg.182]

The two-body dynamics described in the preceding section has been useful in introducing a number of important concepts, and we have obtained valuable insights concerning the angular distribution of scattered particles. However, there is obviously no way to faithfully describe a chemical reaction in terms of only two interacting particles at least three particles are required. Unfortunately, the three-body problem is one for which no analytic solution is known. Accordingly, we must use numerical analysis and computers to solve this problem.7... [Pg.72]

Edelson (1981), using numerical analysis techniques studied the relationship between the period of the B-Z oscillations and the rate constants or initial conditions of the reaction. The principal rate-controlling steps were confirmed numerically to be the enolization and bromination of malonic add. [Pg.86]

This is Laplace s equation in rectangular coordinates. If suitable boundary conditions exist or are known, Eq. (3.9-9) can be solved to give (x, y). Then the velocity at any point can be obtained using Eq. (3.9-5). Techniques for solving this equation include using numerical analysis, conformal mapping, and functions of a complex variable and are given elsewhere (B2, S3). Euler s equations can then be used to find the pressure distribution. [Pg.187]

This model has been successfully used by Chin and Sabde [25] for crevice cathodic protection using numerical analysis based on the dilute solution theory and reduction reaction of dissolved oxygen and Aa+, Cl, and OH ions at the crevice surface. Hence, the Nemst-Plank equation, eq. (4.2), can be generalized as a differentiable and continues scalar diffusion molar flux function... [Pg.272]

The complex soil-structure interaction of underground structures during seismic loading can be simulated using numerical analysis tools which include lumped mass/stif iess methods and finite-element/difference methods. [Pg.2814]


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Numerical analysis

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