applications of ordinary differential equations in computer science

Ngày tải lên: 22/06/2014, 02:20

... 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

... 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: ... vector of dependent variables y(x) from a point x to a point x + H by a sequence of n substeps each of size h, h = H/n (16.3.1) In principle, one could use the modified midpoint method in its ... + 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)...

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) ... vector of dependent variables y(x) from a point x to a point x + H by a sequence of n substeps each of size h, h = H/n (16.3.1) In principle, one could use the modified midpoint method in its ... 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...

Ngày tải lên: 24/12/2013, 12:16

... encountered in practice, is discussed in Đ16.7.) 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 ... 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 ... 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)...

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), Đ 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 ... calculates dydx . { void lubksb(float **a, int n, int *indx, float b[]); void ludcmp(float **a, int n, int *indx, float *d); int i,j,nn,*indx; float d,h,x,**a,*del,*ytemp; indx=ivector(1,n); a=matrix(1,n,1,n); del=vector(1,n); ytemp=vector(1,n); h=htot/nstep;...

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

Ngày tải lên: 19/03/2015, 08:49

... and are interested in finance, insurance and other areas of risk management will find the following flowchart helpful. It suggests the read- ing for an introduction into quantitative methods in nance ... N t made a jump, that is, τ k =inf{t ≥ 0: N t ≥ k} (1.1.23) for k ∈N, t ≥ 0. In some applications, as in the modeling of defaults, the intensity λ t that a certain type of event occurs may depend ... part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in...

Ngày tải lên: 19/02/2014, 22:20

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 28/06/2014, 17:20

Ngày tải lên: 29/06/2014, 13:20

Ngày tải lên: 29/06/2014, 13:20

Ngày tải lên: 29/06/2014, 13:20

... surface [120]. In particular he proves Marr wrong: In general of course, points of inflection in a contour need have no significance for the surface [144]. by showing that inflections of the contour ... Substituting the matching constraint of (2.3~,) into the time derivative of (2.10) we obtain: rt = (At + p.U)p. (2.38) Differentiating (2.38) with respect to time and substituting this into (2.37) ... The numerator is analogous to baseline and the denominator to disparity. In the infinitesimal limit stereo will, in principle, correctly determine the depth of the contour generator. Equation...

Ngày tải lên: 05/03/2014, 15:20

... is no need to intro- duce refolding steps, which is of great advantage since solubilization ⁄ refolding is often a critical step in the production of recombinant proteins. Interestingly the approach ... support in clarifying critical steps of oxidative folding of bovine b-lactoglobulin. b-Lacto- globulin carries five cysteine residues, four of which link in disulfide bridges, raising questions about ... con- formation. In this way, Curtis-Fiske et al. were able to identify native a-helices of the N-terminal 185 residues of the functional domain of the HA2 subunit of the in uenza virus hemagglutinin protein...

Ngày tải lên: 06/03/2014, 00:20

Ngày tải lên: 14/03/2014, 13:20

... conditions of stable and asymptotic equivalence (see [1-5]) of linear delay differential equations under nonlinear perturbation in Banach space. The obtained results thank to use of the theories of general ... ≡ 0 of Eq.(4) is uniformly exponential stable. 2.2. The asymptotic equivalence of linear delay differential equations under nonlinear perturbation in Banach space In this section, we are interested ... are interested in finding conditions such that the solution of Eq.(4) in the case à = 0 will be asymptotic equivalence to the solution of Eq.(4) in the case à = 0 (in the following we will give...

Ngày tải lên: 22/03/2014, 11:20