solving systems of nonlinear ordinary differential equations
Báo cáo hóa học: " Solving systems of nonlinear matrix equations involving Lipshitzian mappings" pdf
Ngày tải lên :
20/06/2014, 22:20
... classes of nonlinear matrix equations (see [8-21]) In this study, we consider the following problem: Find (X1, X2, , Xm) Î (P(n))m solution to the following system of nonlinear matrix equations: ... Duan, F: Positive defined solution of two kinds of nonlinear matrix equations Surv Math Appl 4, 179–190 (2009) Hasanov, V: Positive definite solutions of the matrix equations X ± A*X-q A = Q Linear ... Application of Mathematics in Engineering’24, Proceedings of the XXIV Summer School Sozopol’98.113–116 (1999) Liao, A, Yao, G, Duan, X: Thompson metric method for solving a class of nonlinear matrix...
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báo cáo hóa học:" Research Article Minimal Nonnegative Solution of Nonlinear Impulsive Differential Equations on Infinite Interval" pot
Ngày tải lên :
21/06/2014, 11:20
... investigate the existence of minimal nonnegative solution for a class of second-order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times Consider ... Jurisdiction of Beijing Municipality PHR201008430 , the Scientific Research Common Program of Beijing Municipal Commission of Education KM201010772018 , the 2010 level of scientific research of improving ... impulsive differential equations, ” Nonlinear Analysis: Theory, Methods & Applications, vol 25, no 4, pp 327–337, 1995 D Guo, “Existence of solutions of boundary value problems for nonlinear second...
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Báo cáo hóa học: "ON DISCRETE ANALOGUES OF NONLINEAR IMPLICIT DIFFERENTIAL EQUATIONS" docx
Ngày tải lên :
22/06/2014, 22:20
... analogues of nonlinear implicit differential equations convergence of the explicit Euler method for nonlinear index-1 DAEs is established The results of this section are a nonlinear version” of the ... applied to nonlinear DAEs and PDAEs lead to nonlinear IDEs In this paper the unique solvability of discretized problems obtained via discretization of nonlinear implicit differential equations ... also an index-1 IDE Proof For the proof of the theorem we first reduce (2.6) to its normal form (2.3) Then we will show that (2.3) is of index-1 by verifying all the conditions of Definition 2.1 Let...
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Tài liệu Integration of Ordinary Differential Equations part 1 doc
Ngày tải lên :
15/12/2013, 04:15
... 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...
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Tài liệu Integration of Ordinary Differential Equations part 2 pptx
Ngày tải lên :
15/12/2013, 04:15
... 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 ... email to trade@cup.cam.ac.uk (outside North America) x2 x1 712 Chapter 16 Integration of Ordinary Differential Equations yn yn + Figure 16.1.3 Fourth-order Runge-Kutta method In each step the derivative...
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Tài liệu Integration of Ordinary Differential Equations part 3 doc
Ngày tải lên :
24/12/2013, 12:16
... 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 ... 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 ... Integration of Ordinary Differential Equations for the ith equation will be taken to be ∆0 = eps × yscal[i] (16.2.8) ∆0 = h × dydx[i] (16.2.9) This enforces fractional accuracy not on the values of y...
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Tài liệu Integration of Ordinary Differential Equations part 4 ppt
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 ... The techniques described in this section are not for differential equations containing nonsmooth functions For example, you might have a differential equation whose right-hand side involves a...
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Tài liệu Integration of Ordinary Differential Equations part 5 pdf
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 ... 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 systems...
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Tài liệu Integration of Ordinary Differential Equations part 6 pdf
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 −...
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Tài liệu Integration of Ordinary Differential Equations part 7 pptx
Ngày tải lên :
24/12/2013, 12:16
... Chapter 16 Integration of Ordinary Differential Equations Rosenbrock Methods s y(x0 + h) = y0 + c i ki (16.6.21) i=1 where the corrections ki are found by solving s linear equations that generalize ... 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 ... 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...
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Tài liệu Integration of Ordinary Differential Equations part 8 pdf
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 ... Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall), Chapter [1] Shampine, L.F., and Gordon, M.K 1975, Computer Solution of Ordinary Differential Equations The ... 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...
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ordinary differential equations and dynamical systems - g. teschl
Ngày tải lên :
31/03/2014, 15:56
... §1.1 Newton’s equations §1.2 Classification of differential equations §1.3 First order autonomous equations §1.4 Finding explicit solutions 11 §1.5 Qualitative analysis of first order equations 16 ... integral equations I hope that, after the previous sections, you are by now convinced that integral equations are an important tool in the investigation of differential equations Moreover, the proof of ... 85 90 Part Dynamical systems Chapter §6.1 §6.2 §6.3 §6.4 §6.5 §6.6 Dynamical systems Dynamical systems The flow of an autonomous equation Orbits and invariant sets Stability of fixed points Stability...
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báo cáo hóa học: " Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type" doc
Ngày tải lên :
21/06/2014, 02:20
... conditions x(0) = -x(1) The authors of [20-24] consider this kind of “anti-periodic” conditions for differential equations or impulsive differential equations To the best of our knowledge it is the first ... integro -differential equation of Volterra type on time scales Nonlinear Anal 60, 429–442 (2005) Xing, Y, Ding, W, Han, M: Periodic boundary value problems of integro -differential equations of Volterra ... Advances in Difference Equations 2011, 2011:14 http://www.advancesindifferenceequations.com/content/2011/1/14 Page of 17 It completes the proof Now consider the existence of solutions of PBVP (1.1) It...
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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
... delays,” Journal of Differential Equations, vol 222, no 2, pp 425–438, 2006 12 G Fei, “Multiple periodic solutions of differential delay equations via Hamiltonian systems I,” Nonlinear Analysis: ... inequality For other study of Wirtinger’s inequality, one may see 15 and the references therein Now, we are ready to prove our main results We first give the proof of Theorem 1.3 Proof of Theorem 1.3 From ... and Technology 20070049 References M Han, “Bifurcations of periodic solutions of delay differential equations, ” Journal of Differential Equations, vol 189, no 2, pp 396–411, 2003 R D Nussbaum,...
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Báo cáo hóa học: " Research Article Necessary Conditions of Optimality for Second-Order Nonlinear Impulsive Differential Equations" docx
Ngày tải lên :
22/06/2014, 19:20
... Existence of optimal controls In this section, we not only present the existence of PCl -mild solution of the controlled system (1.1) but also give the existence of optimal controls of systems ... 2 Advances in Difference Equations technique to derive the maximum principle for a Lagrange problem of systems governed by a class of the second-order nonlinear impulsive differential equation ... International Journal of Differential Equations and Applications, vol 1, no 1, pp 37–52, 2000 [3] N U Ahmed, “Necessary conditions of optimality for impulsive systems on Banach spaces,” Nonlinear Analysis,...
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Báo cáo hóa học: " Research Article Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions" potx
Ngày tải lên :
22/06/2014, 19:20
... superlinear growth of the nonlinearity of f (t, p) in p Inspired by [21, 24, 25], in this paper, we investigate the following second-order impulsive nonlinear differential equations with periodic ... ordinary differential equations, ” Nonlinear Analysis, vol 51, no 7, pp 1223–1232, 2002 [24] C Bai, “Existence of solutions for second order nonlinear functional differential equations with periodic ... second order impulsive differential equations, ” Applied Mathematics and Computation, vol 114, no 1, pp 51–59, 2000 [17] L Chen and J Sun, Nonlinear boundary value problem of first order impulsive...
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Báo cáo hóa học: "TERMINAL VALUE PROBLEM FOR SINGULAR ORDINARY DIFFERENTIAL EQUATIONS: THEORETICAL ANALYSIS AND NUMERICAL SIMULATIONS OF GROUND STATES" pdf
Ngày tải lên :
22/06/2014, 22:20
... this paper as “the nature of the vector field.” Therefore, a combination of properties of the associated vector field with the Kneser’s property of the cross sections of the solutions’ funnel is ... the continuation of solutions and the singularity of at the point P0 , the set (P0 ) = ∅ Taking into account the nature of the vector field and the definition of the singularity of the map , this ... (3.3) r →0+ In view of Theorem 2.2 and Remark 2.10, this singular IVP has a local solution By the nature of the vector field (sign of the nonlinearity), any solution ρ = ρ(r) of (3.3) as well as...
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NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
Ngày tải lên :
19/03/2015, 08:49
... x (t ) + k , t + h) School of Chemical Engineering and Advanced Materials Newcastle University 24 Solving sets of • st order ODEs Chemical engineering systems are often described by more than ... accurate solutions The size of the integration interval also influences the accuracy of the solutions (should be less than 10% of the time constant) • • st Solutions of sets of order ODEs are done ... following set of differential equations Example: Multiple Reactions Process • Where k1=0.2 hr -1 and k2=0.1 hr -1 and at time t=0, Ca=1mol/L and Cb=Cc=0mol/L Solve the system of equations and...
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nonlinear analysis & differential equations, an introduction - schmitt & thompson
Ngày tải lên :
31/03/2014, 15:56
... viewed as an extension of Rouche's theorem concerning the equal number of zeros of certain analytic functions This extension will be the content of one of the exercises at the end of thic chapter 16 ... by di erential equations will yield some mathematical explanation of these phenomena (at least in some approximate sense) The intent of this set of notes is to present several of the important ... solutions of various types of problems associated with di erential equations and provide qualitative and quantitative descriptions of solutions At the same time, we develop methods of analysis...
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