Computational methods FORTRAN

D. W. Noid, B. G. Sumpter, B. Wunderlich and G. A. Pfeffer, Molecular dynamics simulations of polymers Methods for optimal Fortran programming , J. Comput. Chem., 11(2), 236-241, 1990. 

In this case besides the integral of Xv, the integral of MAb titer must also be computed. Obviously the same FORTRAN program used for the integration of Xv can also be used for the computations (see Appendix 2). The results by the integral method are shown in Figures 17.12 and 17.13. 

The book explains how to solve coupled systems of ordinary differential equations of the kind that commonly arise in the quantitative description of the evolution of environmental properties. All of the computations that I shall describe can be performed on a personal computer, and all of the programs can be written in such familiar languages as BASIC, PASCAL, or FORTRAN. My goal is to teach the methods of computational simulation of environmental change, and so I do not favor the use of professionally developed black-box programs. 

If/(x) has a simple closed-form expression, analytical methods yield an exact solution, a closed form expression for the optimal x, x. Iff(x) is more complex, for example, if it requires several steps to compute, then a numerical approach must be used. Software for nonlinear optimization is now so widely available that the numerical approach is almost always used. For example, the Solver in the Microsoft Excel spreadsheet solves linear and nonlinear optimization problems, and many FORTRAN and C optimizers are available as well. General optimization software is discussed in Section 8.9. 

The actual program used at NPL was written by N.P. Barry on the basis of the methods described previously. It is written in FORTRAN and has been implemented on IBM 370 and UNIVAC 1100 computers operated by computer bureaux. Vector algebra is employed. The reason why the graphs have double boundaries is that the calculation can be performed for boundaries of any convex polygon of up to 30 sides. This permits calculations to be restricted to the stability range of particular components, for example, that of water or chloride. 

The FORTRAN program ARTHUR (Harper et al. 1977)—running on main frame computers at this time—comprised all basic procedures of multivariate data analysis and made these methods available to many chemists in the late 1970s. 

In order to compare the present technique with the method based on the Ifeilman filter (jt), the same examples presented in that publication will be attempted. The first two examples are synthetic, while the third is based on real experimental data. All examples were solved by means of a VAX 11/780 computer programmed in FORTRAN 77. Routines for matrix operation from the IMSL package (28) were utilized. 

A computer program for the solution of the FOS equation, which is a modification of the method of Fuoss, Onsager, and Skinner (5), was written in Fortran IV and executed on an IBM System 360/50 (Operating System—H Level) computer. The program uses the method of Wentworth (35) for least-squares... 

One of the authors (D.H. Chen, Department of Chemical Engineering, Lamar University, Beaumont, Texas 77710), has written a computer program incorporating this complete estimation method and it is available for a nominal fee. This Fortran-based program is an executable program that will run out of DOS on an IBM-compatible PC. Structural input to the program is via a series of queries the user must respond to. Some familiarity with the estimation method is necessary to properly use the computer program. 

For both the subdistribution and the GEX fit methods a Marquardt algorithm for constrained non-linear regression was used to minimize the sum of squares error (.10). The FORTRAN program CONTIN was used for the constrained regularization method. All computations were performed on a Harris H-800 super mini computer. 

G. Beech, Fortran IV in Chemistry An Introduction to Computer-Assisted Methods, Wiley, Chichester, 1975. 

A FORTRAN program is available from the authors. For each system, uj are assigned for species in phases expected at equilibrium. As uj become small for all species in a phase, variables are retained and new values computed using Powell s method. 

Recently, a new version of ADSA-P has been developed [67.681 that is superior to the original program in terms of computation time and range of applicability. The new version is written in the C language (rather than FORTRAN) and utilizes more efficient and accurate numerical methods. For example, the new algorithm uses the curvature at the apex (rather than the radius of curvature), it permits an additional optimization parameter (the vertical misalignment of the camera), and it gives improved initial estimates of the apex location and shape. 

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