application of ordinary differential equation in real life

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Ngày tải lên: 10/08/2014, 05:21

... America). Chapter 16. Integration of Ordinary Differential Equations 16.0 Introduction Problems involving ordinary differential equations (ODEs) can always be reduced to the study of sets of first-order differential ... 1973, Computational Methods in Ordinary Differential Equations (New York: Wiley). Lapidus, L., and Seinfeld, J. 1971, Numerical Solution of Ordinary Differential Equations (New York: Academic ... 708 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C)...

Ngày tải lên: 15/12/2013, 04:15

... 1973, Computational Methods in Ordinary Differential Equations (New York: Wiley). Lapidus, L., and Seinfeld, J. 1971, Numerical Solution of Ordinary Differential Equations (New York: Academic ... discussion of the pitfalls in constructing a good Runge-Kutta code is given in [3] . Here is the routine for carrying out one classical Runge-Kutta step on a set of n differential equations. You input ... derive from this basic 712 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C)...

Ngày tải lên: 15/12/2013, 04:15

... Minimizing lateness/tardiness • Minimizing makespan • Maximizing system/machine utilization • Minimizing WIP (work in process) • Maximizing throughput • Minimizing average flow time • Minimizing ... routings. A routing is selected such that the following goals are achieved: • Minimizing number of blocked machines. • Minimizing total processing time. • Minimizing number of processing steps Four ... Simulation of scheduling rules in a flexible manufacturing system using fuzzy logic, IEA-AIE96 Ninth International Conference on Industrial and Engineering Application of Artificial Intelligence...

Ngày tải lên: 17/12/2013, 06:15

... methods. free_vector(ytemp,1,n); free_vector(ak6,1,n); free_vector(ak5,1,n); free_vector(ak4,1,n); free_vector(ak3,1,n); free_vector(ak2,1,n); } Noting that the above routines are all in single precision, don’t be too greedy in specifying eps. Thepunishment forexcessive greediness is interestingand worthyof Gilbertand Sullivan’sMikado: ... + H, z n )] (16.3.2) 714 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall), Chapter 2. [2] Shampine, L.F., and Watts, H.A. 1977, in Mathematical Software III ,...

Ngày tải lên: 24/12/2013, 12:16

... 722 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... hmin) nrerror("Step size too small in odeint"); h=hnext; } nrerror("Too many steps in routine odeint"); } CITED REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial ... H/n (16.3.1) In principle, one could use the modified midpoint method in its own right as an ODE integrator. In practice, the method finds its most important application as a part of the more powerful...

Ngày tải lên: 24/12/2013, 12:16

... remind you once again that scaling of the variables is often crucial for successful integration of differential equations. The scaling “trick” suggested in the discussion following equation (16.2.8) ... extrapolate each component of a vector of quantities. 728 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... encountered in practice, is discussed in §16.7.) 726 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright...

Ngày tải lên: 24/12/2013, 12:16

... 734 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... is a particular class of equations that occurs quite frequently in practice where you can gain about a factor of two in efficiency by differencing the equations directly. The equations are second-order ... FURTHER READING: Stoer, J., and Bulirsch, R. 1980, Introduction to Numerical Analysis (New York: Springer-Verlag), § 7.2.14. [1] Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential...

Ngày tải lên: 24/12/2013, 12:16

... as in the original Bulirsch-Stoer method. The starting point is an implicit form of the midpoint rule: y n+1 − y n−1 =2hf  y n+1 + y n−1 2  (16.6.29) 738 Chapter 16. Integration of Ordinary Differential ... methods have been, we think, squeezed 740 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... Example of an instability encountered in integrating a stiff equation (schematic). Here it is supposed that the equation has two solutions, shown as solid and dashed lines. Although the initial conditions...

Ngày tải lên: 24/12/2013, 12:16

... methods have been, we think, squeezed 752 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... methods in all applications. We are willing, however, to be corrected. CITED REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, ... method .In functional iteration, we take some initial guess for y n+1 , insert it into the right-hand side of (16.7.2) to get an updated value of y n+1 , insert this updated value back into the...

Ngày tải lên: 24/12/2013, 12:16

... risk of being left behind. Simply, CRM is a high-tech way of gathering mou- ntains of information about customers, then using it to make customers happy—or at least a source of more business. ... on behalf of human users to perform laborious and routine tasks such as locating and accessing neces- sary information, resolving inconsistencies in the retrieved information, filtering away irrelevant and ... irrelevant and unwanted information, and integrating infor- mation from heterogeneous information sources. In order to execute tasks on behalf of a business process, computer application, or an individual, agents...

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Ngày tải lên: 17/03/2014, 16:20

... other measures of individual in- come uncertainty: the income quintile share ratio (income of the 20% richest to income of 20% poorest), the percentage of working households in the risk of poverty ... though the decline in the lending rate, higher uncertainty deters individuals from taking loans, and the share of household credit in GDP declines from 14.3% to 13.4%. If individual uncertainty is low, ... reflects the life- cycle profiles of income and consumption. In initial periods, when income is relatively low, individuals are taking loans as they expect that their income will increase in the future....

Ngày tải lên: 29/03/2014, 06:21

... stability of the following func- tional equation f (mx + ny)= (m + n)f(x + y) 2 + (m − n)f(x − y) 2 (1) in various spaces, which was introduced and investigated in [13]. 2. Preliminaries In this ... there exists a mapping A : X ® Y satisfying the following: (1) A is a fixed point of J, that is, A  x m  = 1 m A(x ) (5) for all x Î X. The mapping A is a unique fixed point of J in the set  = ... there exists a mapping A : X ® Y satisfying the following: (1) A is a fixed point of J, that is, A  x m  = 1 m A(x ) (12) for all x Î X. The mapping A is a unique fixed point of J in the set  =...

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