applications of differential equations in biology ppt

Ngày tải lên: 21/06/2014, 01:20

... 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 ... 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 ... 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

... 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 ... step h instead of the two required by second-order Runge-Kutta. Perhaps there are applications where the simplicity of (16.3.2), easily coded in- line in some other program, recommends it. In general,...

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 ... 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; ... 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...

Ngày tải lên: 24/12/2013, 12:16

... ntegrable on the interval I deter- mined by roots of a(x); (3) a(x)p(x )vanishesattheendpointsofI and, in case there is an end point at infinity, the product a(x)p(x)P(x) should vanish at infinity for ... is integrable on the entire interval. The integrability of the weight function determines the differential equation and finiteness of the norm of poly nomials ensures that manipulations as in ... in every degree which is an eigenfunction of L. Specializing to second-order equations because of their importance in applications and leaving in this article the higher-order case because of...

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Ngày tải lên: 10/08/2014, 21:22

Ngày tải lên: 10/08/2014, 21:22

Ngày tải lên: 10/08/2014, 21:22

Ngày tải lên: 10/08/2014, 21:22

... flaring blazing The reduplication decreasing intensity: ã nh nhố nh: soft mild (less) ã xinh xinh xinh: pretty cute ã o : red reddish ã xanh xanh xanh: blue/green bluish/ greenish ã In ... time and scope, we have introduced some features of English morpheme system as well as its importance in learning English in general and spelling, developing vocabulary in particular. It’s also ... supermarket ã Second, some morphemes in the 2 language can increase or decrease the intensity of verbs, adjectives… E.g.: The reduplication increasing intensity: ã au au ing: hurt agony ã mnh mnh...

Ngày tải lên: 08/04/2013, 09:31

... evolution of the larger-scale features of interest takes place superposed with a kind of “frozen in (though fluctuating) background of small-scale stuff. This answer gives a differencing scheme ... form again and in practice usually retains the stability advantages of fully implicit differencing. Schr ă odinger Equation Sometimes the physical problem being solved imposes constraints on ... evolve through of order λ 2 /(∆x) 2 steps before things start to happen on the scale of interest. This number of steps is usually prohibitive. We must therefore find a stable way of taking timesteps...

Ngày tải lên: 15/12/2013, 04:15

... underlying PDEs, perhaps allowing second-order spatial differencing for first-order -in- space PDEs. When you increase the order of a differencing method to greater than the order of the original ... Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machine- readable files (including this ... America). are using is known to be extremely stable, we do not recommend anything higher than second-order in time (for sets of first-order equations) . For spatial differencing, we recommend the order of the...

Ngày tải lên: 15/12/2013, 04:15

... level of CR, we have reduced the number of equations by a factor of two. Since the resulting equations are of the same form as the original equation, we can repeat the process. Taking the number of ... y-values on these x-lines. Then fill in the intermediate x-lines as in the original CR algorithm. The trick is to choose the number of levels of CR so as to minimize the total number of arithmetic operations. ... mentioned in Đ19.0, relaxation methods involve splitting the sparse matrix that arises from finite differencing and then iterating until a solution is found. There is another way of thinking about...

Ngày tải lên: 15/12/2013, 04:15

... F lying outside K i . 2. The two endpoints of k lie in distinct boundary components of pairs of pants. The first thing to notice is that the arc of the boundary of the disk ex- tending E in Γ ... ball B embedded in M so that there is a nontrivial cycle of Γ contained in the interior of B. Then F is reducible. Proof. Let C be the nontrivial cycle of Γ contained in the interior of B. Notice ... indexed planes from P and reindex the remaining ones by N in an order preserving manner. TOPOLOGICAL CLASSIFICATION OF MINIMAL SURFACES 683 The main result in [8] is: Theorem 2.1 (The Ordering...

Ngày tải lên: 16/02/2014, 06:20