NAG library

The ordinary differential equations for f and C now form a fifth-order system which can be solved using a standard NAG library routine. The results are shown in Fig. 10.73. This figure also shows the numerical results for concentration obtained using a full numerical approach, and there is reasonable agreement between the two. 

Equations (15)-(23) can be solved numerically using a combination of IMSL and NAG library subroutines. The DIVPAG subroutine of IMSL for ordinary differential equations and the D03PAF subroutine of NAG library for partial differential equations may serve the purpose and we applied this method for simulating the results for ELM extraction of CPC [26] and cephalexin [25]. The agreement between model prediction and experimental data was found to be quite reasonable. 

Due to its remarkable sparseness, the matrix H from Eq. (130) is easy to diagonalize even for higher dimensions. In this way, we have explicitly obtained very accurate eigenvalues [uk f=1 for K 1000 [38,39] via the NAG library [50]. However, the same library fails when we used its corresponding routine in an attempt to directly root polynomials of much lower degrees, K > 120. 

This is an iterative method that calculates the next set of values by direct elimination. A small matrix [N] is added to the coefficient matrix [M] so that [M + N] is easily factored with much less arithmetic than performing elimination on [M]. An iteration parameter controls the amount of N added. The method is more economical and the convergence rate is much less sensitive to the iteration parameter than SOR. Subroutines for 2d and 3d SIP may be found in the NAG library (D03EBF and D03ECF). 

The mathematical model that derives from equations (1-3) has been solved numerically by means of routines available in the NAG library. The range of parameter values for which oscillations appear has been found by using the software AUTO. 

With each set of variables at any point, we have calculated 30 independent realizations of 30 x 30 x 30 random networks. Nevertheless, even with a high number of independent realizations of random networks the results have in any case a small variance. The performance index was calculated in all cases within the boundaries for seven different radii of the micropores and seven different microporosities. The performance indices calculated were fitted by a two-dimensional spline function. For this purpose we have taken the E02DAF routine from the NAG library. The spline coefficients were then read by an optimization routine, written by the present authors, based on the COMPLEX method of Box [1]. We would like to stress that it is very important to include the corrections in eq. (10) and (11). Otherwise, one would not obtain reasonable optimization results. 

Fortran sub-routine E04 FBF NAG library, NAG Ltd., Oxford). A preliminary grid search was made to check for irregularities in the sum of squares surface and provide a starting point for the search. 

Model calculations comprised the solution of the system of the differential Eqs. (31) and (35) for the case of sorption equilibrium as well as (34) and (35) for the kinetic case (non-equilibrium). Calculations were performed by computer programs in FORTRAN 77 with the aid of the subroutine D03PGF from the NAG-library on the IBM-computer system ES/9600-620 of the research center. The subroutine D03PGF employs Gear s method for the numerical solution of differential equations. 

The three-dimensional model network is based on a cubic lattice. The lengths of the pores are all equal to one unit and the radii of the pores are allocated as random values from a log-normal distribution using a NAG library routine. A pseudo-random generator is used with a fixed seed so that reproducible runs can be achieved. Reduced connectivity was achieved by randomly deleting pores from a network by "knock-out", and blind pores were created by blocking access to a node at one end of the pore. 

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