system of ordinary differential equations second order

... 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 ... 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

... available at the end of the article Abstract In this article, we study the existence of positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders ⎧ ⎪ −Dα+ ... Difference Equations 2011, 2011:10 http://www.advancesindifferenceequations.com/content/2011/1/10 RESEARCH Open Access Positive solutions for a coupled system of nonlinear differential equations of mixed ... fractional orders Yige Zhao1, Shurong Sun1,2*, Zhenlai Han1,3 and Wenquan Feng1 * Correspondence: sshrong@163 com School of Science, University of Jinan, Jinan 250022, Shandong, PR China Full list of

Ngày tải lên: 21/06/2014, 03:20

... 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 yi t Fi t, y1 , y2 , y3 , , yn ... coefficients of like powers of p, we get the following set of equations: coefficient of p0 : Y0 ∞ L−1 ai,n Pn t , 3.11 n coefficient of p1 : Y1 L−1 fi i L−1 Yi,1 − L−1 Ni Yi,0 i i Now, we solve these equations ... various kinds of nonlinear equations The new homotopy perturbation method NHPM was applied to linear and nonlinear ODEs 17 In this paper, we construct the solution of system of fractional -order differential

Ngày tải lên: 21/06/2014, 05:20

... ordinary differential equations Chapter PRELIMINARIES 1.1 Introduction In this thesis, we explore the stability of ordinary differential equations And we will consider differential equations in the ... set of x A(x) The α-limit set of x Γ Simple closed curve (or periodic orbit) T Period iv Bachelor thesis PHUNG THI HONG LIEN Preface Differential equations are one of the most important areas of ... instability of an orbit A more general method is the Lyapunov function In fact, any one of the numbers of different stabilization standards is used Therefore, we will study the stability of ordinary differential

Ngày tải lên: 23/12/2019, 16:17

... ordinary differential equations Chapter PRELIMINARIES 1.1 Introduction In this thesis, we explore the stability of ordinary differential equations And we will consider differential equations in the ... set of x A(x) The α-limit set of x Γ Simple closed curve (or periodic orbit) T Period iv Bachelor thesis PHUNG THI HONG LIEN Preface Differential equations are one of the most important areas of ... instability of an orbit A more general method is the Lyapunov function In fact, any one of the numbers of different stabilization standards is used Therefore, we will study the stability of ordinary differential

Ngày tải lên: 07/04/2021, 08:05

... doi:10.1155/2011/192156 Research Article Existence and Uniqueness of Periodic Solution for Nonlinear Second- Order Ordinary Differential Equations Jian Zu College of Mathematics, Jilin University, Changchun 130012, ... and uniqueness of a periodic solution for secondorder ordinary differential equations with some assumption Introduction The study on periodic solutions for ordinary differential equations is a ... about the existence of periodic solutions for second- order differential equations have been obtained by combining the classical method of lower and upper solutions and the method of alternative problems

Ngày tải lên: 14/07/2023, 09:44

... at bookboon.com Second- order ordinary differential equations Contents Contents Preface to these three texts Part I The series solution of second order, ordinary differential equations and special ... Second- order ordinary differential equations Special functions, Sturm-Liouville theory and transforms R.S Johnson Download free books at R.S Johnson Second- order ordinary differential equations ... Touche LLP and affiliated entities D Second- order ordinary differential equations Contents List of Equations 67 Introduction and Background 68 1.1 The second- order equations 68 1.2 The boundary-value

Ngày tải lên: 16/12/2017, 10:40

... 2009. 10 Advances in Difference Equations 22 T. Li, Z. Han, and S. Sun, “Oscillation of one kind of second- order delay dynamic equations on time scales,” Journal of Jishou University, vol. 30, ... of second- order delay dynamic equations on time scales 8–22. 2 Advances in Difference Equations In this work, we will consider the existence of nonoscillatory solutions to the second- order neutral ... in Dynamic Equations on Time Scales,Birkh ¨ auser, Boston, Mass, USA, 2003. 5 L. Erbe, “Oscillation results for second- order linear equations on a time scale,” Journal of Difference Equations

Ngày tải lên: 21/06/2014, 20:20

... Difference Equations Volume 2009, Article ID 907368, 16 pages doi:10.1155/2009/907368 Research Article Existence of Weak Solutions for Second- Order Boundary Value Problem of Impulsive Dynamic Equations ... type. However, to the best of our knowledge, few papers have been published on the existence of solutions for second- order boundary value problem of impulsive dynamic equations on time scales via ... existence results for second- order boundary value problem of impulsive differential equations on time scales by using Schaefer’s fixed point theorem and nonlinear alternative of Leray-Schauder type.

Ngày tải lên: 21/06/2014, 20:20

... solutions of second- order difference equations, ” Journal of Mathematical Analysis and Applications, vol 141, no 2, pp 463–483, 1989 3 T Peil and A Peterson, “Criteria for C-disfocality of ... of. .. Ekvacioj, vol 39, no 3, pp 491–517, 1996 12 M Cecchi, M Marini, and G Villari, “On the monotonicity property for a certain class of second order differential equations, ” Journal of ... of second order quasilinear difference equations, ” Funkcialaj Ekvacioj, vol 39,... H Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, vol 65 of

Ngày tải lên: 22/06/2014, 06:20

... solutions of second- order difference equations, ” Journal of Mathematical Analysis and Applications, vol 141, no 2, pp 463–483, 1989 3 T Peil and A Peterson, “Criteria for C-disfocality of ... of. .. Ekvacioj, vol 39, no 3, pp 491–517, 1996 12 M Cecchi, M Marini, and G Villari, “On the monotonicity property for a certain class of second order differential equations, ” Journal of ... of second order quasilinear difference equations, ” Funkcialaj Ekvacioj, vol 39,... H Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, vol 65 of

Ngày tải lên: 22/06/2014, 19:20

... Proof. By the continuation of solutions and the singularity of ᏷ at the point P 0 , the set ᏷(P 0 ) = ∅. Taking into account the nature of the vector field and the definition of the singularit y of ... this paper as “the nature of the vec- tor field.” Therefore, a combination of properties of the associated vector field with the Kneser’s property of the cross sections of the solutions’ funnel ... the singular point P0 of the map ᏷∗ is unique, then the uniqueness of the point... Two-point boundary value problems for higher -order linear differential equations with strong singularities,

Ngày tải lên: 22/06/2014, 22:20

... MATH 3036- DIFFERENTIAL EQUATIONS Lecturer : Dr Nguyễn Hữu Thọ Department of Mathematics - WRU Slide 11 - Unit Introduction to Differential Equations Dr Nguyen Huu Tho - Department of Mathematics ... Chapter Introduction to Differential Equations 1.1 Differential Equations Models Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - Dr Nguyen Huu Tho - Department of Mathematics Slide 11 ... to solve Differential Equations Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - 276 Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - 277 Dr Nguyen Huu Tho - Department of Mathematics

Ngày tải lên: 16/12/2020, 00:10

... MATH 3036- DIFFERENTIAL EQUATIONS Lecturer : Dr Nguyễn Hữu Thọ Department of Mathematics - WRU Slide 11 - Unit Introduction to Differential Equations Dr Nguyen Huu Tho - Department of Mathematics ... Chapter Introduction to Differential Equations 1.1 Differential Equations Models Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - Dr Nguyen Huu Tho - Department of Mathematics Slide 11 ... to solve Differential Equations Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - 276 Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - 277 Dr Nguyen Huu Tho - Department of Mathematics

Ngày tải lên: 21/03/2021, 18:30

... Trang 1 Periodic solutions of some linear evolution systems of natural differential equations on 2-dimensional tore Dang Khanh Hoi* Department of General Education, Hoa Binh University, ... 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 ... bundle of manifolds X, C°(€) is the space of smooth differential forms and H*(€) is the Sobolev space of differential forms over X (see, [4]) By A we denote operator i(d+0), so-called natural differential

Ngày tải lên: 14/03/2014, 13:20

... §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 ... Linear autonomous first order systems 47 §3.3 General linear first order systems 50 §3.4 Periodic linear systems 54 iii iv Contents Chapter §4.1 §4.2 §4.3 §4.4 Differential equations in the complex ... map, 106 e flow of a dynamical system, 101 principal matrix of a linear system, 51 the set of reals shift map on ΣN , 202 spectrum (set of eigenvalues) of a matrix sequence space

Ngày tải lên: 31/03/2014, 15:56

... made available soon. Further 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 ... order of entire solutions of some algebraic differential equations and improve the related results of Bergweiler, Barsegian, and others. We also estimate the growth order of entire solutions of ... algebraic differential equations of higher order. In 2009, Yuan et al. [9], improved their results and gave a general estimate of order of w(z), which depends on the degrees of coefficients of differential

Ngày tải lên: 20/06/2014, 20:20

... asymptotic stability of the nonlinear impulsive stochastic differential equations and the impulsive stochastic partial differential equations with infinite delays by means of the fixed point theory ... results on stability of the zero solution of Equation Then, we generalized the results of the stability to Equation Consider the first -order delay neutral differential equation of the form x (t) ... Advances in Difference Equations 2011, 2011:48 http://www.advancesindifferenceequations.com/content/2011/1/48 RESEARCH Open Access New criteria for stability of neutral differential equations with variable

Ngày tải lên: 20/06/2014, 22:20

... nonnegative numbers System (1) was mentioned in [1] as one of three systems of Open Problem 3, which asked for a description of the global dynamics of some rational systems of difference equations In ... Handbook of Differential Equations: Ordinary Differential Equations, vol II, pp 239–357 Elsevier, Amsterdam (2005) 10 Kalabušić, S, Kulenović, MRS, Pilav, E: Global dynamics of a competitive system of ... for global dynamics of the System (1) is determining the basins of attraction of different equilibrium points The difficulty in analyzing the behavior of all solutions of the System (1) lies in

Ngày tải lên: 21/06/2014, 00:20

... made available soon. Further 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 ... order of entire solutions of some algebraic differential equations and improve the related results of Bergweiler, Barsegian, and others. We also estimate the growth order of entire solutions of ... algebraic differential equations of higher order. In 2009, Yuan et al. [9], improved their results and gave a general estimate of order of w(z), which depends on the degrees of coefficients of differential

Ngày tải lên: 21/06/2014, 17:20