numerical solutions of ordinary differential equations

... 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 ... from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Note that for compatibility with bsstep the arrays y and d2y are of length 2n for a system of n second-order equations ... scales of the independent variable on which the dependent variables are changing For example, consider the following set of equations[1]: u0= 998u + 1998v with boundary conditions By means of the

Ngày tải lên: 24/12/2013, 12:16

... 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

... instability of an orbit A more generalmethod is the Lyapunov function In fact, any one of the numbers ofdifferent stabilization standards is used Therefore, we will study thestability of ordinary differential ... Trang 1DEPARTMENT OF MATHEMATICS———o0o——— PHUNG THI HONG LIEN STABILITY OF ORDINARY DIFFERENTIAL EQUATIONS BACHELOR THESIS Hanoi – 2019 Trang 3Thesis AcknowledgementI ... outcome of the experiment too much Thesystem is stable, since the particle starts near the origin On the other hand, the differential equations are an approximation tothe true equations of motion

Ngày tải lên: 07/04/2021, 08:05

... analysis of the positivity of solutions and the establishment of the exponential stability conditions for the positive equilibrium of such systems.This study addresses the positivity of solutions ... investigates the positivity of solutions and exponential stability of positive equilibrium in nonlinear differential equations with delays, focusing on various types of neural networks The main ... 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 equation

Ngày tải lên: 31/07/2024, 16:30

... Trang 1MINISTRY OF EDUCATION AND TRAININGHANOI NATIONAL UNIVERSITY OF EDUCATION ——————–o0o——————— LE THI HONG DUNG STABILITY OF POSITIVE SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAYS ... is concerned with the positivity of solutions and exponential stability ofpositive equilibrium of nonlinear differential equations with delays in various types of neuralnetworks Main contribution ... positive solutions and stability of nonlinear differential equations withdelays B Research aims The thesis focuses on problems of stability of several classes of nonlinear positive ential systems

Ngày tải lên: 31/07/2024, 17:01

... 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

... existence and uniqueness of solutions of a class of fractional differential equations J Math Anal Appl 334 (2007) 1–10. 8 Momani, SM, Ibrahim, RW: On a fractional integral equation of periodic functions ... in Difference Equations © 2012 Ibrahim ; licensee Springer. Trang 2Extremal solutions for certain type of fractional differential equations with maxima Rabha W Ibrahim Institute of Mathematical ... the existence of extremal solutions for fractional differential equations with maxima 1 Introduction Fractional calculus has become an exciting new mathematical method of solution of diverse problems

Ngày tải lên: 21/06/2014, 17:20

... e-neighborhood of the point 0 in C' Trang 1026 D.K Hoi / WU Journal of Science, Mathematics - Physics 26 (2010) 17-27Proof Let K be a compact operator; we fix 6 > 0 The structure of the spectrum of a ... phrases: Natural differential operators, small denominators, spectrum of compact oDerators. 1 Introduction Beside authors, as from A.A Dezin (see, [1]), considered 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 in the classical space.

Ngày tải lên: 14/12/2017, 14:55

... Fractional Differential Equations 21 2.1 Main result 21 2.2 Existence of Solutions 22 2.3 Uniqueness of Solutions 25 Bibliography 28 Trang 6LIST OF SYMBOLSN Set of natural ... Trang 2HANOI PEDAGOGICAL UNIVERSITY 2DEPARTMENT OF MATHEMATICS ——————–o0o——————— NGUYEN THI HAO ON THE EXISTENCE OF SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS GRADUATION THESIS Speciality: Analysis ... 1HANOI PEDAGOGICAL UNIVERSITY 2 DEPARTMENT OF MATHEMATICS——————–o0o——————— NGUYEN THI HAO ON THE EXISTENCE OF SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS GRADUATION THESIS Speciality: Analysis

Ngày tải lên: 23/12/2019, 16:17

... 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

... DIFFERENTIAL EQUATIONS Lecturer : Dr Nguyễn Hữu Thọ Department of Mathematics - WRU Trang 2Slide 11 - 2 Dr Nguyen Huu Tho - Department of Mathematics Unit 1 Introduction to Differential Equations ... Nguyen Huu Tho - Department of Mathematics Trang 26Slide 11 - 26 Dr Nguyen Huu Tho - Department of Mathematics Unit 2 Differential Equations and solutions Separable Equations Trang 28Slide 11 ... Dr Nguyen Huu Tho - Department of Mathematics Trang 46Slide 11 - 46 Dr Nguyen Huu Tho - Department of Mathematics Unit 3 Linear Equations Exact Differential Equations Trang 47Slide 11 - 47

Ngày tải lên: 21/03/2021, 18:30

... systems of differential equations,” Proceedings of the Royal Society of Edinburgh Section A, vol 78, no 1-2, pp 139–159, 1977. 6 Y Liu and W Ge, “Positive periodic solutions of nonlinear Duffing equations ... 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 problemsThe ... fferential Equations, vol 180, no 1, pp 51–64, 2002. 3 R Kannan and V Lakshmikantham, “Existence of periodic solutions of nonlinear boundary value problems and the method of upper and lower solutions,”

Ngày tải lên: 14/07/2023, 09:44

... short) of the i“ investor Denote the position of the 7 investor at the end of the nTM time interval by s;(n) = +1, and the sense or sentiment of the market by the average of the states of all of ... models of phenomena in almost every scientific discipline, and their efficient and reliable numerical solution is greatly desired.High-order numerical methods for solving ordinary differential equations ... theory of financial markets [3] An essential part of his thesis was the modeling of the distribution of price changes of a financial asset These he assumed to be Gaussian, using the theory of Brownian

Ngày tải lên: 02/10/2024, 01:54

... Trang 18 Numerical Solutions of the Black Scholes Equation (i) The object of this chapter is to explain various methods of solving the Black Scholes equation by numerical methods, and ... turning to these, it is worth pointing out to the reader that the numerical solution of partial differential equations is something of an art form, containing many hidden pitfalls We explain the ... seemingly unrelated line of reasoning This should of course be of no great surprise: rThe binomial model is a graphical way of approximating the probability density function of a stock price (or

Ngày tải lên: 25/10/2013, 19:20

... of solutions In fact, equations in three (ormore) dimensions will often exhibit chaotic behavior which makes a simpledescription of solutions impossible! Problem 1.21 Generalize the concept of ... the differential equation for y = y(x) you have to solve.) 1.5 Qualitative analysis of first order equations As already noted in the previous section, only very few ordinary differentialequations ... 2004 Copyright c Trang 4§1.2 Classification of differential equations 5§1.3 First order autonomous equations 8 §1.5 Qualitative analysis of first order equations 16 §2.2 The basic existence and

Ngày tải lên: 31/03/2014, 15:56

... 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 ... decay rates of the solutions Keywords: fixed points, stability, neutral differential equation, variable delays 1 Introduction The objective of this article is to investigate the stability of the zero ... for stability of neutral differential equations with variable delays by fixed points method Dianli Zhao1,2 Correspondence: Tc_zhaodianli@139.com 1 College of Science, University of Shanghai for

Ngày tải lên: 20/06/2014, 22:20

... rewarding, and the results about these equations offer prototypes towards the development of the basic theory of the global behavior of nonlinear differ-ence equations of a big order, recently, many ... models of a second class of diseases associated with the produc-tion of red cells, white cells, and platelets in the bone marrow The study of the nonlinear rational difference equations of a higher ... some special cases of this equation Keywords: Stability, Solutions of the difference equations 1 Introduction The purpose of this article is to investigate the global attractivity of the equilibrium

Ngày tải lên: 21/06/2014, 00:20

... of first-order partial differential equations, including questions such as estimates of solutions of initial problems, estimates of domains of solutions, estimates of the difference between solutions ... 2functions of one variable, which are solutions of ordinary differential equations orinequalities There exist many generalizations of the above classical results We list some of them below Differential ... by means of functions of one variable which are solutions of ordinary differential equations or inequalities It is shown that there are solutions of initial problems defined on the Haar pyramid

Ngày tải lên: 21/06/2014, 02:20

... differential equations by extending the idea of17,18 This method leads to computable and efficient solutions to linear and nonlinear operator equations The corresponding solutions of the integer-order equations ... coefficients of like powers of p, we get the following set of equations: coefficient of p0: Y0 L−1 ∞  n 0 , coefficient of p1 : Y1 L−1 i   L−1 i Y i,1 − L−1 i Ni Y i,0 . 3.11 Now, we solve these equations ... 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 D α i y i t  F i  f i t, y i t0

Ngày tải lên: 21/06/2014, 05:20