Computational mathematics

E. Hairer and G. Wanner. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, volume 14 of Springer Series in Computational Mathematics. Springer-Verlag, New York, New York, second edition, 1996. 

The product form of equation 5.1-6, and its assumed lognormal-distribution make the fragility computations mathematically tractable. 

Rt is ironic that such an intensely computational mathematical science as chaos theory owes much of its modern origin to calculations that were performed not on a large mainframe computer but rather a simple programmable pocket calculator, a Hewlett-Packard HP-65 Feigenbaum would explain years later that had the series of intermediate calculations not been carried out sufficiently slowly, it is likely that most of the key observations would have been missed [feigSOa]. 

Before the advent of modem computer-aided mathematics, most mathematical models of real chemical processes were so idealized that they had severely limited utility— being reduced to one dimerrsion and a few variables, or Unearized, or limited to simplified variability of parameters. The increased availability of supercomputers along with progress in computational mathematics and numerical functional analysis is revolutionizing the way in which chemical engineers approach the theory and engineering of chemical processes. The means are at hand to model process physics and chenustry from the... 

Marchuk, G. (1975) Methods of Computational Mathematics. Springer New York. 

A rough description of the term modeling is the process of applying methods well-developed in computational mathematics to real-life situa-... 

Schittkowski, K. Computational Mathematical Programming. Springer-Verlag, Berlin (1985). 

J.E.Dennis, R.B. Schnabel Numerical methods for unconstrained optimization and non-linear equations, Prentice Hall Series in computational mathematics, New York, (NY, USA), 1983... 

The main advantage of PCR over inverse MLR is that it accounts for covariance between different x variables, thus avoiding any potential problems in the model computation mathematics, and removing the burden on the user to choose variables that are sufficiently independent of one another. From a practical viewpoint, it is much more flexible than CLS, because it can be used to develop regression models for any property, whether it is a concentration property or otherwise. Furthermore, one needs only the values of the property of interest for the calibration samples (and not the concentrations of aU components in the samples). 

Varga, R. S., "Gerschgorin and His Circles, Springer Series in Computational Mathematics, 36". Springer, Berlin (2004). 

S. V. Branovitskaya, R. B. Medvedev, and Yu. Ya. Fialkov, Computing Mathematics in Chemistry and Chemical Engineering, Vishcha Shkola, Kiev, 1986. 

Zaika Yu.V. (1996) The solvability of the equations for a model of gas transfer through membranes with dynamic boundary conditions, Computer Mathematics and Math. Physics 36(12), 1731-1741. 

The MEIS developers relying on the capabilities of modem computers and computational mathematics started the work whichresulted in an essential expansion of the application area of "good, old" classical thermodynamics and in the possibility to study (using thermodynamics) any states on all possible motion trajectories of a nonequilibrium system. In other words, they put forward the goal to use the models of equilibrium not only to determine the directions of irreversible processes but to estimate the attainability of desired and undesired states on these directions. 

S.A. Hovanessian, Computational Mathematics in Engineering, Lexington Books, Toronto, 1976. 

J. Murphy and B. McShane, Computational Mathematics Applied to Numerical Methods, Prentice-Hall, Upper Saddle River, NJ (1998) J. L. Mohamed and J. E. Walsh, Numerical Algorithms, Oxford Univ. Press, New York (1986). 

J. Murphy and B. McShane, Computational Mathematics Applied to Numerical Methods, Prentice-Hall, Upper Saddle River, NJ (1998). 

Combinatorial and Computational Mathematics Center Pohang University of Science and Technology... 

Dmitriev, V. I., Editor in chief, 1990, Computational mathematics and techniques in exploration geophysics (in Russian) Nedra, Moscow, 498 pp. 

Mathematical calculation, based on quantum mechanics, was established in the 1920s and developed with the rapid progress and spread of computers. Mathematical calculation is the field in which the approximated equation is solved by computers. 

E. J. Weniger and B. Kirtman, in Numerical Methods in Physics, T. E. Simos, G. Avdelas, and J. Vigo Aguiar, eds.. Chemistry and Engineering. Computers Mathematics with Applications, Elsevier, Holland, 2002. 

Analytical procedure for empty cylinder of Functionally Graded Material(FGM) with axial symmetry has been investigated. Based on thermal elasticity theory and computational mathematical method, temperature distribution has been obtained and thermal stress of FGM in ring section has been calculated. 

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