ten real world applications of differential equations

... 36 Real- World Applications of Genetic Algorithms 3.1 Design of FSS using fractal geometries FSS with fractal elements has attracted the attention of microwave engineering researchers because of ... yield) Real- World Applications of Genetic Algorithms In terms of multi-objective optimization, GA was used for solving the scalar optimization problem based on the principle of survival of the ... particularly of interest for the rapid large scale 28 Real- World Applications of Genetic Algorithms production of low-cost high performance microwave devices reducing or eliminating the need of post...

Ngày tải lên: 27/06/2014, 05:20

... of a delay differential equation, while in the second example, we will obtain the bound of the solutions of an integral equation For the sake of proving the global existence of solutions of differential ... and Feng Journal of Inequalities and Applications 2011, 2011:20 http://www.journalofinequalitiesandapplications.com/content/2011/1/20 Page of 15 Theorem B: Under the hypothesis of Theorem B, if ... the Zheng and Feng Journal of Inequalities and Applications 2011, 2011:20 http://www.journalofinequalitiesandapplications.com/content/2011/1/20 Page 13 of 15 uniqueness of solutions cannot be guaranteed...

Ngày tải lên: 21/06/2014, 01:20

... terms of the numbers of people who subscribe to, owe allegiance to, or co-author the contending discourses: a discourse that commands the reflective assent of only some of the people, or only of ... a person shares some of the characteristics of a class of persons; To indicate that a person symbolizes the identity or qualities of a class of persons Starting at the end of this list and working ... results of a micro-deliberative process recommending one course of action, and a petition of 150,000 signatories demanding another The question of methods of choice is bound up with the question of...

Ngày tải lên: 11/06/2014, 00:01

... visualization algorithms in real- time modes using a DSP The core of the EVM DM642™ is a digital media processor that is characterized by a large set of integrated features of the card, such as: a ... 2Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow, Russia Page 10 of 10 18 I Ideses, L Yaroslavsky, Three methods that improve the visual quality of colour anaglyphs ... defined by the convolution of spline θN-1 (x) and AF up(x) in the interval [-(N+2)/2, (N+2)/ 2] Thus, fupN(x) can be written in the following form: fupN (x) = Page of 10 M v V=2 (−1) sin (2m...

Ngày tải lên: 20/06/2014, 22:20

... −8 −6 −4 −2 10 10 t (s) t (s) Figure 6: Time-frequency distribution of x(t) of Figure Figure 4: Solution of (6), real part of x(t), when the forcing term is f (t) = A exp(iβt /2) + B exp(iγ4 ... much better understood in the phase-space of time frequency Such bilinear transformations have been studied for over Figure 7: Solution of (6), real part of x(t), for a sinusoidal frequency modulated ... obtain the compact form of (18) and (19) The combined use of (24)–(27) allows one to obtain (17) Now, we take the bilinear distribution of the left- and right-hand sides of (15) to obtain CP(D)x,P(D)x...

Ngày tải lên: 23/06/2014, 01:20

Ngày tải lên: 06/07/2014, 15:18

Ngày tải lên: 11/03/2015, 07:57

... solutions of differential equations have been studied since the very beginning of this century The theory of almost periodic solutions has been developed in connection with problems of differential equations, ... existence of almost periodic solutions of almost periodic evolution equations by using stability properties of nonautonomous dynamical systems Sections and of this chapter extend the concept of ... uniformly in BC(R, X) Proof 1.3.3 For the proof see e.g [7, p 9] Sprectrum of an Almost Periodic Function There is a natural extension of the notion of Fourier exponents of periodic functions to...

Ngày tải lên: 29/10/2015, 12:32

... by a lot of researchers see 7–13 Most of the work contained in literature on 1.1 is the existence and multiplicity of periodic solutions However, except the questions of the existence of periodic ... 2 Journal of Inequalities and Applications For the special case that n and p 1, various problems on the solutions of 1.1 , such as the existence of periodic solutions, bifurcations of periodic ... “Existence of periodic solutions of one-dimensional differential-delay equations, ” Tohoku Mathematical Journal, vol 30, no 1, pp 13–35, 1978 S Chapin, “Periodic solutions of differential-delay equations...

Ngày tải lên: 22/06/2014, 02:20

... Một số hàm đặc biệt Lý thuyết giải tích phân số (Theory of fractional caculus) Phương trình vi phân phân thứ (Fractional differential equations) Báo cáo hoàn thành hướng dẫn tận tình TS HÀ BÌNH ... Chương 3: Phương trình vi phân phân thứ (Fractional differential equations) 1 7 12 12 12 16 ... ) + a2 ) 29 Nguyễn Thị Hằng k35 CN Toán Chương Phương trình vi phân phân thứ (Fractional differential equations) Trong chương này, ta xét phương trình vi phân phân thứ bậc (n, q) 3.1 3.1.1 Phương...

Ngày tải lên: 19/12/2014, 19:28

... long-term safety of DESs remains in question (10-11) Despite the results of meta-analyses of randomized studies refuting these concerns (12), late stent thrombosis remains a limitation of DES technology ... have shown that a potential problem with the DES is late in-stent thrombosis (20) Multiple studies have shown that the use of antiplatelet agents decreases the risk of in-stent thrombosis in DES ... al Safety of direct stenting with the Endeavor stent: results of the Endeavor II continued access registry EuroIntervention, 2007; 3: 76–81 Kandzari DE, Leon MB, Popma JJ Comparison of Zotarolimus-eluting...

Ngày tải lên: 25/10/2012, 11:18

... subject of stiff equations, relevant both to ordinary differential equations and also to partial differential equations (Chapter 19) Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... 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 Press) ... value problem Each comes with its own set of debits and credits that must be understood before it is used 710 Chapter 16 Integration of Ordinary Differential Equations CITED REFERENCES AND FURTHER...

Ngày tải lên: 15/12/2013, 04:15

... uninteresting countryside The resulting gains in efficiency are not mere tens of percents or factors of two; they can sometimes be factors of ten, a hundred, or more Sometimes accuracy may be demanded not ... sequence of steps in identical manner Prior behavior of a solution is not used in its propagation This is mathematically proper, since any point along the trajectory of an ordinary differential ... free_vector(dym,1,n); 714 Chapter 16 Integration of Ordinary Differential Equations } CITED REFERENCES AND FURTHER READING: Abramowitz, M., and Stegun, I.A 1964, Handbook of Mathematical Functions, Applied...

Ngày tải lên: 15/12/2013, 04:15

... problems of the fictional What A Hamburger! Actual 30 THE REAL WORLD OF FINANCE companies in the restaurant business provide a real- world look at applications of cash flow statement analysis Of course, ... or 20 THE REAL WORLD OF FINANCE sales Assume that the fictional What A Hamburger! chain had total sales of $1.2 billion, requiring $600 million of equity capital If your SBU or group of restaurants ... most of these online companies (i.e., Webvan) failed.4 Vague Plans Several dot.coms have had vague business plans, spending tens of millions of dollars trying to find a viable strategy Often the...

Ngày tải lên: 18/12/2013, 09:12

... generally useful stepper routine is this: One of the arguments of the routine will of course be the vector of dependent variables at the beginning of a proposed step Call that y[1 n] Let us require ... steps each of size h) Since the basic method is fourth order, the true solution and the two numerical approximations are related by 716 Chapter 16 Integration of Ordinary Differential Equations ... steps (see Figure 16.2.1) How much overhead is this, say in terms of the number of evaluations of the right-hand sides? Each of the three separate Runge-Kutta steps in the procedure requires...

Ngày tải lên: 24/12/2013, 12:16

... powers of h, 724 Chapter 16 Integration of Ordinary Differential Equations } CITED REFERENCES AND FURTHER READING: Gear, C.W 1971, Numerical Initial Value Problems in Ordinary Differential Equations ... method does an excellent job of feeling its way through rocky or discontinuous terrain It is also an excellent choice for quick-and-dirty, low-accuracy solution of a set of equations A second warning ... with the advantage of requiring (asymptotically for large n) only one derivative evaluation per step h instead of the two required by second-order Runge-Kutta Perhaps there are applications where...

Ngày tải lên: 24/12/2013, 12:16

... method a degree of robustness for problems with discontinuities Let us remind you once again that scaling of the variables is often crucial for successful integration of differential equations The ... Second-Order Conservative Equations Usually when you have a system of high-order differential equations to solve it is best to reformulate them as a system of first-order equations, as discussed ... 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...

Ngày tải lên: 24/12/2013, 12:16

... 16 Integration of Ordinary Differential Equations Note that for compatibility with bsstep the arrays y and d2y are of length 2n for a system of n second-order equations The values of y are stored ... vol 27, pp 505–535 16.6 Stiff Sets of Equations As soon as one deals with more than one first-order differential equation, the possibility of a stiff set of equations arises Stiffness occurs in ... 16.5 Second-Order Conservative Equations 733 Here zm is y (x0 + H) Henrici showed how to rewrite equations (16.5.2) to reduce roundoff error by using the quantities ∆k ≡ yk+1 −...

Ngày tải lên: 24/12/2013, 12:16

... email to trade@cup.cam.ac.uk (outside North America) x 736 Chapter 16 Integration of Ordinary Differential Equations Of course, we give up accuracy in following the evolution towards equilibrium ... generalized to sets of linear equations with constant coefficients: y = −C · y (16.6.9) yn+1 = (1 − Ch) · yn (16.6.10) Now a matrix An tends to zero as n → ∞ only if the largest eigenvalue of A has magnitude ... classes of higher-order methods for stiff systems: • Generalizations of the Runge-Kutta method, of which the most useful are the Rosenbrock methods The first practical implementation of these...

Ngày tải lên: 24/12/2013, 12:16

... The second of the equations in (16.7.9) is 752 Chapter 16 Integration of Ordinary Differential Equations you suspect that your problem is suitable for this treatment, we recommend use of a canned ... Chapter 16 Integration of Ordinary Differential Equations For multivalue methods the basic data available to the integrator are the first few terms of the Taylor series expansion of the solution at ... fixed number of iterations (say, one) is an explicit method! When we fix the number of iterations in advance, then the final value of yn+1 can be written as some complicated function of known quantities...

Ngày tải lên: 24/12/2013, 12:16