français apos s method of solving differential equations
Báo cáo hóa học: " New criteria for stability of neutral differential equations with variable delays by fixed points method" docx
Ngày tải lên :
20/06/2014, 22:20
... t s e− h(u)du s d s τ (s) h(u)x(u)du b (s) p (s − τ (s) ) + c (s) p (s − τ (s) ) − p (s) + p (s − τ (s) )(1 − τ (s) ) p (s) t t p (s − τ (s) ) c (s) × z (s − τ (s) )ds + e− s h(u)du dz (s − τ (s) ) p (s) − τ (s) ... + σ t s e− h(u)du h (s) z (s) ds − τ (s) ) + c (s) p (s − τ (s) ) − p (s) z (s − τ (s) )ds p (s) t p (s − τ (s) ) s h(u)du c (s) z (s − τ (s) )ds p (s) t s h(u)du b (s) p (s Performing an integration by parts, we ... h (s) ϕ (s) ds t s h(u)du t s h(u)du −β (s) + h s − τ (s) − τ (s) − r (s) ϕ t − τ (t) ds s h (s) s τ (s) h(u)ϕ(u)du ds Next, we prove Q Î S Let be small and Î S, then there are constants δ, L >0 such...
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Báo cáo hóa học: " Research Article On Efficient Method for System of Fractional Differential Equations" potx
Ngày tải lên :
21/06/2014, 05:20
... decomposition method having integral w.r.t dξ α ,” Journal of King Saud University—Science In press 20 A S Bataineh, M S M Noorani, and I Hashim, Solving systems of ODEs by homotopy analysis method, ” ... corresponding solutions of the integer-order equations are found to follow as special cases of those of fractional-order equations We consider the system of fractional-order equations of the form Dαi ... Integro-Differential equations 13 , nonlinear dispersive K m, n, equations 14 , Long Porous Slider equation 15 , and Navier-Stokes equations 16 It can be said that He s homotopy perturbation method is a universal...
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Báo cáo hóa học: " Research Article A Generalized Wirtinger’s Inequality with Applications to a Class of Ordinary Differential Equations" docx
Ngày tải lên :
22/06/2014, 02:20
... 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 solutions, ... p is also considered 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 ... differential equation 1.2 has been done to the best of the author knowledge Motivated by these cases, as a part of this paper, we study the estimates of periods of periodic solutions for the differential...
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Tài liệu Integration of Ordinary Differential Equations part 1 doc
Ngày tải lên :
15/12/2013, 04:15
... rkqs, bsstep, stiff, and stifbs are steppers; rkdumb and odeint are drivers Section 16.6 of this chapter treats the subject of stiff equations, relevant both to ordinary differential equations ... derivatives (right-hand sides of the equations) multiplied by stepsizes In this chapter we consider three major types of practical numerical methods for solving initial value problems for ODEs: • ... Stoer, and so extrapolation methods are often called Bulirsch-Stoer methods Predictor-corrector methods store the solution along the way, and use those results to extrapolate the solution one step...
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Tài liệu Integration of Ordinary Differential Equations part 2 pptx
Ngày tải lên :
15/12/2013, 04:15
... ODE integrator should exert some adaptive control over its own progress, making frequent changes in its stepsize Usually the purpose of this adaptive stepsize control is to achieve some predetermined ... about strict mathematics That is, it reflects the nature of the problems that contemporary scientists like to solve For many scientific users, fourth-order Runge-Kutta is not just the first word ... makes it easy to incorporate Runge-Kutta into relatively simple “driver” schemes We consider adaptive stepsize control, discussed in the next section, an essential for serious computing Occasionally,...
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Tài liệu Integration of Ordinary Differential Equations part 3 doc
Ngày tải lên :
24/12/2013, 12:16
... [Taylor series expansion tells us the φ is a number whose order of magnitude is y(5) (x)/5!.] The first expression in (16.2.1) involves (2h)5 since the stepsize is 2h, while the second expression ... independently, as two half 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 ... adaptive stepsize control Integrate starting values ystart[1 nvar] from x1 to x2 with accuracy eps, storing intermediate results in global variables h1 should be set as a guessed first stepsize,...
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Tài liệu Integration of Ordinary Differential Equations part 4 ppt
Ngày tải lên :
24/12/2013, 12:16
... Gragg It turns out that the error of (16.3.2), expressed as a power series in h, the stepsize, contains only even powers of h, 724 Chapter 16 Integration of Ordinary Differential Equations } CITED ... beyond our scope here Apart from those two caveats, we believe that the Bulirsch-Stoer method, discussed in this section, is the best known way to obtain high-accuracy solutions to ordinary differential ... solution of a set of equations A second warning is that the techniques in this section are not particularly good for differential equations that have singular points inside the interval of integration...
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Tài liệu Integration of Ordinary Differential Equations part 5 pdf
Ngày tải lên :
24/12/2013, 12:16
... 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 ... extrapolated to zero stepsize The sequence of separate attempts to cross the interval H is made with increasing values of n, the number of substeps Bulirsch and Stoer originally proposed the sequence 727 ... different sequences of finer and finer substeps Their results are extrapolated to an answer that is supposed to correspond to infinitely fine substeps In the Bulirsch-Stoer method, the integrations are...
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Tài liệu Integration of Ordinary Differential Equations part 6 pdf
Ngày tải lên :
24/12/2013, 12:16
... stoerm using the same arguments; just be sure that the argument nv of bsstep is set to 2n You should also use the more efficient sequence of stepsizes suggested by Deuflhard: (16.5.6) and set KMAXX ... arrays y and d2y are of length 2n for a system of n second-order equations The values of y are stored in the first n elements of y, while the first derivatives are stored in the second n elements ... at xs) in its first n elements Its second n elements are not referenced Also input is htot, the total step to be taken, and nstep, the number of substeps to be used The output is returned as yout[1...
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Tài liệu Integration of Ordinary Differential Equations part 7 pptx
Ngày tải lên :
24/12/2013, 12:16
... 16.6 Stiff Sets of Equations y Figure 16.6.1 Example of an instability encountered in integrating a stiff equation (schematic) Here it is supposed that the equation has two solutions, shown as solid ... differencing gives In general this is some nasty set of nonlinear equations that has to be solved iteratively at each step Suppose we try linearizing the equations, as in Newton s method: yn+1 = ... systems: • Generalizations of the Runge-Kutta method, of which the most useful are the Rosenbrock methods The first practical implementation of these ideas was by Kaps and Rentrop, and so these methods...
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Tài liệu Integration of Ordinary Differential Equations part 8 pdf
Ngày tải lên :
24/12/2013, 12:16
... case: high-precision solution of very smooth equations with very complicated right-hand sides, as we will describe later Nevertheless, these methods have had a long historical run Textbooks are ... multistep methods Consider first the question of stepsize adjustment To change stepsize from h to h at some point xn , simply multiply the components of yn in (16.7.5) by the appropriate powers of ... for stiff problems functional iteration will not even converge unless we use tiny stepsizes, no matter how close our prediction is! Thus Newton iteration is usually an essential part of a multistep...
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Tài liệu Numerical Solution of Stochastic Differential Equations with Jumps in Finance pdf
Ngày tải lên :
19/02/2014, 22:20
... processes and homogeneous Poisson processes, while other authors analyze the larger class of SDEs driven by fairly general semimartingales The class of SDEs driven by Wiener processes and Poisson ... tree-based, and finite difference methods The class of SDEs considered here are those driven by Wiener processes and Poisson random measures Some authors consider the smaller class of SDEs driven ... process is the most basic stochastic process that allows us to model continuous uncertainty, as it arises for instance as trading noise Note that SDEs with Jumps the Wiener process is not a stationary...
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Báo cáo "On the asymptotic behavior of delay differential equations and its relationship with C0 - semigoup " potx
Ngày tải lên :
22/03/2014, 11:20
... equations, Scientis publishing house Anma-Ata, 1974 (Russian) [13] N.T Hoan, Asymptotic equivalence of systems of differential equations, IZV.Acad Nauk ASSR (1975) 35 (Russian) [14] C.K Sung, H.G ... The asymptotic equivalence of functional differenttial equations, J Differenttial Equat (1996) 306 [3] E.V Voskoresenski, Asymptotic equivalence of systems of differential equations, Results of ... Journal of Science, Mathematics - Physics 23 (2007) 63-69 Main results 2.1 The uniformly stable of null solution of delay differential equations Let us consider the delay differential equations dx(t)...
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galois theory of linear differential equations - m. van der put, m. singer
Ngày tải lên :
31/03/2014, 15:56
... union of intersections of open and closed subsets (See also the discussion following Exercises A.9) In this special case, this means that the image of a is either finite or co-finite Since a−c is invertible ... fundamental set of solutions of L(y) = 0, whose field of constants is the same as that of k such that no proper subfield contains a fundamental set of solutions of L(y) = 1.4 The Differential Galois Group ... points having this monodromy representation? This is one form of Hilbert s 21st Problem and we describe its positive solution We discuss refined versions of this problem that demand the existence of...
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Báo cáo toán học: " Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations" docx
Ngày tải lên :
20/06/2014, 20:20
... results of the estimate of growth of entire solutions of some classes of algebraic differential equations Qi Jianming1,3 , Li Yezhou2 and Yuan Wenjun∗3 Department of Mathematics and Physics, Shanghai ... Barsegian, and others We also estimate the growth order of entire solutions of a type system of a special algebraic differential equations We give some examples to show that our results are sharp ... Math Sci (in press, in Chinese) 17 [11] Gu, RM, Ding, JJ, Yuan, WJ: On the estimate of growth order of solutions of a class of systems of algebraic differential equations with higher orders J Zhanjiang...
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Báo cáo hóa học: " Positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders" pot
Ngày tải lên :
21/06/2014, 03:20
... study of coupled systems involving fractional differential equations is also important as such systems occur in various problems, see [22-30] Bai and Fang [24] considered the existence of positive ... follows In Sect 2, we shall give some definitions and lemmas to prove our main results In Sect 3, we establish existence results of at least one or two positive solutions for boundary value problem ... existence results of positive solutions for boundary value problem (1.1) Consider the following coupled system of integral equations: ⎧ ⎪ ⎪ u(t) = ⎪ ⎨ ⎪ ⎪ v(t) = ⎪ ⎩ G1 (t, s) f (s, v (s) ) ds,...
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báo cáo hóa học:" Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations" ppt
Ngày tải lên :
21/06/2014, 17:20
... results of the estimate of growth of entire solutions of some classes of algebraic differential equations Qi Jianming1,3 , Li Yezhou2 and Yuan Wenjun∗3 Department of Mathematics and Physics, Shanghai ... Barsegian, and others We also estimate the growth order of entire solutions of a type system of a special algebraic differential equations We give some examples to show that our results are sharp ... Math Sci (in press, in Chinese) 17 [11] Gu, RM, Ding, JJ, Yuan, WJ: On the estimate of growth order of solutions of a class of systems of algebraic differential equations with higher orders J Zhanjiang...
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báo cáo hóa học:" Extremal solutions for certain type of fractional differential equations with maxima" pptx
Ngày tải lên :
21/06/2014, 17:20
... control of various technical systems It often occurs that the law of regulation depends on maximum values of some regulated state parameters over certain time intervals Many studies of the existence ... existence of solutions are imposed such as periodicity, asymptotic stability and oscillatory [10–12] In [13], the authors discusses the existence of univalent solutions for fractional integral equations ... examples of applications in differential and integral equations and inclusions, physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, engineering, dynamical systems, control...
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