applications of ordinary differential equations in physics

... 1NUMERICAL SOLUTIONSOF ORDINARY DIFFERENTIAL EQUATIONS Trang 2ODEs in Chemical Engineering• The ODEs that occur in Chemical Engineering tend to be of the following form: • Following the previous ... method)Trang 25Solving sets of 1st order ODEs• Chemical engineering systems are often described by more than 1 ODE, e.g dynamic material and energy balances • At each integration interval, the equations ... accurate solutions • The size of the integration interval also influences the accuracy of the solutions (should be less than 10% of the time constant) • Solutions of sets of 1st order ODEs are done

Ngày tải lên: 19/03/2015, 08:49

... true equations of motion We will be interested in finding whetherthe solutions of slightly different equations give the same basis solutionstructure Thus we could investigate the effect of adding ... tend to infinity in finite time We caninfer to this idea of stability the system is unstable, not because solutiondiverge, but because the solution of the original equations are different in character ... Trang 14y = ˙rsinθ + r ˙sinθi.e ˙y = ˙rsinθ + r ˙θcosθ Multiplying the second equation by −sinθ, the fourth equation by cosθ We have − ˙xsinθ = ˙rsinθcosθ + r ˙θsin2θ, ˙ycosθ = ˙rsinθcosθ + r ˙θcos2θ

Ngày tải lên: 23/12/2019, 16:17

... structure of the dis-sertation consists of three chapters equa-Chapter I: Presenting basic knowledge of delay differential equations Chapter II: Methods of solving delay differential equations ... studying the model of HIV transmission in cells Chapter III: Studying the application of delay differential equation in HIVtransmission model This is the main content of the dissertation and finallyconclusion ... the model is a system of one ordinary differential equation and one with delay differential tions.The models studied are: General model, ordinary differential equationmodel, differential equation

Ngày tải lên: 03/03/2021, 19:53

... true equations of motion We will be interested in finding whetherthe solutions of slightly different equations give the same basis solutionstructure Thus we could investigate the effect of adding ... tend to infinity in finite time We caninfer to this idea of stability the system is unstable, not because solutiondiverge, but because the solution of the original equations are different in character ... Trang 14y = ˙rsinθ + r ˙sinθi.e ˙y = ˙rsinθ + r ˙θcosθ Multiplying the second equation by −sinθ, the fourth equation by cosθ We have − ˙xsinθ = ˙rsinθcosθ + r ˙θsin2θ, ˙ycosθ = ˙rsinθcosθ + r ˙θcos2θ

Ngày tải lên: 07/04/2021, 08:05

... radius of the spherical interfaces between the fluidphases of the same substance An interval of the parameter, in which there is a strictlyincreasing and positive solution defined on the half-line, ... loss of generality) as Trang 3results on existence and multiplicity of the singular BVPtwo-Using in this paper a quite different approach, we are going to prove, the existence of an increasing ... equicontinuous family sinceProof Let B : = {( t, u, v) : t ≥0, max{ u − ρ0 , v } < 1 } We associate to any P ∈[0, T] × R 2, the closest pointQ in B This is obviously a continuous mapping Defining

Ngày tải lên: 22/06/2014, 22:20

... nicepresentation of methods as well as results in the area In recent years, there has been an increasing interest in extending certain classical results to differential equations in Banach spaces In this ... abstract functional differential equations with infinitedelay, there are three kinds of definitions of stabilities In Sections 3 and 4, we provesome equivalence of these definitions of stabilities ... the case of almost periodic solutions of (linear and nonlinear)equations in Banach spaces To this end, in the first chapter we present introduc-tions to the theory of semigroups of linear operators

Ngày tải lên: 29/10/2015, 12:32

... variation-of-constants formula in the theory of linear ordinary differential equations So, we often call the representation formula obtained here the variation-of-constants formula in the phase space Such ... is finite dimensional, the representation formula for functional differential equations has been established by Hale [5] in the case of finite delay and by Murakami [16] in the case of infinite ... admissibility of some spaces of functions whose spectra are contained in a closed subset of the real line © 2002 Elsevier Science Key Words: functional differential equations; phase space; variation-of-constants

Ngày tải lên: 17/12/2017, 16:49

... page intentionally left blankThis page intentionally left blank Trang 3Perturbation of the Boundary in Boundary-Value Problemsof Partial Differential Equations Trang 5Managing Editor: Professor ... Simplicity of Eigenvalues of the Dirichlet vii Trang 106.6 Generic Simplicity of Eigenvalues of Robin’s Problem 946.7 Generic Simplicity of Solutions of
u + f (u, x) = 0 in , 7.6 Calculation of some ... ball in Rn with radius r and center (r /σ)k, while B1/2 concentric ball with radius r/2 Then every point of R n is contained in some B k1/2 , and no point is contained in more than (2σ + 1) n of

Ngày tải lên: 04/03/2019, 11:09

... contribute to influencing our future Come and join us in reinventing light every day. Light is OSRAM Trang 5A First Course in Ordinary Differential Equations 5 Contents 3.1 Introduction: the initial- ... Chapter 1 Linear differential equations and linearly independent solutions In this chapter we define the different types of solutions that we will encounter in ourstudies of differential equations ... φ2= sin2x, φ3= 1} is linearly dependent for all x ∈ R Then −2 cos x sin x 2 sin x cos x 0 2 sin2x− 2 cos2x 2 cos2x− 2 sin2x 0 Trang 22A First Course in Ordinary Differential Equations 22 Linearity

Ngày tải lên: 15/01/2021, 09:11

... contribute to influencing our future Come and join us in reinventing light every day. Light is OSRAM Trang 5A First Course in Ordinary Differential Equations 5 Contents 3.1 Introduction: the initial- ... Chapter 1 Linear differential equations and linearly independent solutions In this chapter we define the different types of solutions that we will encounter in ourstudies of differential equations ... φ2= sin2x, φ3= 1} is linearly dependent for all x ∈ R Then −2 cos x sin x 2 sin x cos x 0 2 sin2x− 2 cos2x 2 cos2x− 2 sin2x 0 Trang 22A First Course in Ordinary Differential Equations 22 Linearity

Ngày tải lên: 15/01/2021, 09:12

... Existence and Uniqueness of Periodic Solution for Nonlinear Second-Order Ordinary Differential Equations Jian Zu College of Mathematics, Jilin University, Changchun 130012, China Correspondence should ... of Di fferential Equations, vol 9, pp 67–85, 1971. 5 H W Knobloch and K Schmitt, “Non-linear boundary value problems for systems of differential equations,” Proceedings of the Royal Society of ... Methods & Applications, vol 59, no 1-2, pp 133–146, 2004. 9 K Schmitt, “Periodic solutions of linear second order differential equations with deviating argument,” Proceedings of the American

Ngày tải lên: 14/07/2023, 09:44

... devel- oped Its intrinsic interest and relevance has been found in a variety of disciplines like mechanics, physics, chemistry, ecology or artificial intelligence.Appearing naturally in practice, ... computationally In addition, because of the infinite-dimensional nature of the phase space, the qualitative study of time-delay systems becomes much more complicated than that of ordinary differential ... of nonlinear neuronal systems with delays remains a significant area of interest in systems and control theory Despite progress in understanding positive systems, challenges persist in studying

Ngày tải lên: 31/07/2024, 16:30

... 1MINISTRY OF EDUCATION AND TRAININGHANOI NATIONAL UNIVERSITY OF EDUCATION ——————–o0o——————— LE THI HONG DUNG STABILITY OF POSITIVE SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAYS IN ... been derived in the form of linear programingwith M-matrices Trang 26CONCLUDING REMAKRSThis thesis focuses on the problem of stability of nonlinear differential equations withdelays in neural networks ... problem of a positive equilibriumpoint of the BAM-Cohen-Grosberg system with time-varying delays Chapter 3 investigatesthe problem of the exponential stabilization of nonlinear delay differential equations

Ngày tải lên: 31/07/2024, 17:01

... the linear differential equations on manifolds in which includes the external differential operators At research of such equations appear so named the small denominators, so such equations is incorrect ... fixed ) 1s dominated by ôyỐ„, where Sz = Sz(L) is the sum of all integers m satisfying (12) Summing an arithmetic progression, we obtain Considering the union of the intervals in question over ... is incorrect in the classical space There is extensive literature on the different types of the equations, in which appear small denominators We shall note, in particular, work of B.I Ptashnika

Ngày tải lên: 14/03/2014, 13:20

... One of the most puzzling ideas in elementary calculus is the idea of the differential In the usual definition, the differential of a dependent variable y = f(x), is given in terms of the differential ... yields the familiar differential of area in polar coordinates 2 The differential of area in polar coordinates is a special example of the change of coordinate theorem for multiple integrals It is ... count the dimensions of the space of k-forms in R” in the sense of vector spaces We will thing of 0-forms as being ordinary functions Since functions are the *scalars”, the space of 0-forms as a vector

Ngày tải lên: 27/03/2014, 11:52

... an introduction to ordinary differentialequations and dynamical systems We start with some simple examples of explicitly solvable equations Then we prove the fundamental resultsconcerning the initial ... called of second order since the highestderivative is of second degree More precisely, we even have a system ofdifferential equations since there is one for each coordinate direction In our case ... y0(x) = sin(y)x + cos(x) (iii) y0(x) = sin(x)y + cos(x) Problem 1.4 Find the most general form of a second order linear equation.Problem 1.5 Transform the following differential equations into first

Ngày tải lên: 31/03/2014, 15:56

... that of a classifier with an infinitenumber of learning samples Consider a learning set of m patterns Each a machine learning algorithm results in finding an optimum set of meters p The machine ... of patterns This situation is illu-strated in Figure 17.In general, for each linearly separable training set, one can find an infinitenumber of hyperplanes that discriminate the two classes of ... situated in the space region delimited by the 1 margin are not important in defining the SVM model, and they can be eliminated from the training setwithout changing the SVM solution The use of nonlinear

Ngày tải lên: 02/06/2014, 09:46

... results of the estimate of growth of entire solutions of some classes of algebraic differential equations Advances in Difference Equations 2012, 2012:6 doi:10.1186/1687-1847-2012-6 Oi Jiaming (qijianmingdaxia@163.com) ... For information about publishing your research in Advances in Difference Equations go to http://www.advancesindifferenceequations.com/authors/instructions/ For information about other SpringerOpen ... Republic of China 2School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, People’s Republic of China University, Guangzhou 510006, People’s Republic of China Email

Ngày tải lên: 20/06/2014, 20:20

... asymptotic stability of the non-linear impulsive stochastic differential equations and the impulsive stochastic partial differential equations with infinite delays by means of the fixed point theory On ... Proof By choosingh (t) =0.05 3+t and p(t) = 1 + sin2(t) in Theorem 3.1, we have    p t − τ(t) p(t) c(t) 1− τ(t)   = 1 + sin2 t−π 2 1 + sin2t sin 2t =2− sin 2(t) 1 + sin2t sin 2t≤ ... Fixed point and exponential p-stability of neutral stochastic differential equations with multiple delays Proceedings of the 2010 IEEE International Conference on Intelligent Computing and Intelligent

Ngày tải lên: 20/06/2014, 22:20

... solutions on different kinds of deterministic differential equations have been considerably investigated in lots of publications [5-15] because of its signifi-cance and applications in physics, mechanics, ... Our main result is established by using fractional powers of linear operators and Banach contraction principle The obtained result can be seen as a contribution to this emer-ging field since it ... studied in [23] We first use a sharper definition (Definition 2.1) of square-mean almost auto-morphic process than the Definition 2.5 in [23] We then present some additional properties of square-mean

Ngày tải lên: 21/06/2014, 03:20