power series solution of ordinary differential equations

... the propagation of derivative discontinuities through systems of equations is presented. Following a short resumd of standard techniques for the solution of ordinary differential equations (ODE's), ... The Numerical Solution of Delay -differential Equations by David Richard Wille Department of Mathematics University of Manchester volume I of II A thesis submitted to the University of Manchester ... for the solution of systems of delay -differential equations. A novel representation for the differential equation is used to acknowledge structural differences between delay- and ordinary differential

Ngày tải lên: 11/10/2014, 04:02

... The Numerical Solution of Delay -differential Equations by David Richard Wile Department of Mathematics University of Manchester volume II of II A thesis submitted to the University of Manchester ... appendix we give a formal proof of the result (1.1.3:14). For any given time let the order of continuity of the component y i be Z i . Our task is thus to obtain a set of lower bounds {c i : > ... closure of E. Heuristically, by an extension of the above arguments, we may think of Ei as defining the set of points whose continuity bounds can affect the continuity bound, c i , of y i .

Ngày tải lên: 11/10/2014, 04:03

... 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 ... has solution x = c.e−t is an integral curve Definition 1.3.3 Suppose that x˙ = f (x) The solution of this differential equation define a flow, ϕ(x, t), such that ϕ(x, t) is solution of the differential ... 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 ... has solution x = c.e−t is an integral curve Definition 1.3.3 Suppose that x˙ = f (x) The solution of this differential equation define a flow, ϕ(x, t), such that ϕ(x, t) is solution of the differential ... 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

... 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 ... 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, ... 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

... 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 ... consequently, ρ is a local solution of (2.6).  Taking into account the classical theorem of the extendability of solutions, we impose one more condition on the desired solution lim r→+∞ p(r)ρ  ... 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 is the

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

... Research Article Bernstein Series Solution of a Class of Lane-Emden Type Equations Osman Rasit Isik1 and Mehmet Sezer2 Elementary Mathematics Education Program, Faculty of Education, Mugla Sitki ... classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain A matrix method was given by Yuzbasi for solving nonlinear LaneEmden type equations ... by means of the relation (27), as follows: 𝜉 ∈ (0, 𝑅) (35) If 𝑝𝑛 is the Bernstein series solution of (2), then it satisfies (2) ̃ = G ̃ on the nodes So, 𝑝𝑛 and 𝑝𝑛 𝑓 are the solutions of WA ̃A

Ngày tải lên: 01/11/2022, 08:57

... (outside North America). A ⋅ x = b SVD ? ?solution? ?? of A ⋅ x = c solutions of? ?? A ⋅ x = c′ solutions of? ?? A ⋅ x = d null space of A  SVD solution of? ?? A ⋅ x = d range of A d c (b) (a) A x b c′ Figure ... the same permutation of the columns of U,elementsofW,andcolumnsofV(or rows of V T ), or (ii) forming linear combinations of any columns of U and V whose corresponding elements of W happen to be ... combination of the set of equations that we are trying to solve. The resolution of the paradox is that we are throwing away precisely a combination of equations that is so corrupted by roundoff error

Ngày tải lên: 24/12/2013, 12:16

... also be aware of some of the special sparse forms that occur in the solutionof partial differential equations in two or more dimensions. See Chapter 19. If your particular pattern of sparsity is ... applications.) • Each of the first N locations of ija stores the index of the array sa that contains the first off-diagonal element of the corresponding row of the matrix. (If there are no off-diagonal ... parameter γ = −b 1 to avoid loss of precision by subtraction in the first of equations (2.7.11). In the unlikely event that this causes loss of precision in the second of these equations, you can make

Ngày tải lên: 24/12/2013, 12:16

... 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 ... and close Let € = OF gf? = OP gAM(T*X) @C is the complexified cotangent bundle of manifolds X, C°(€) is the space of smooth differential forms and H*(€) is the Sobolev space of differential forms

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 ... York, 1973 [5] C Chicone, Ordinary Differential Equations with Applications, Springer, New York, 1999 [6] E.A Coddington and N Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New ... Characteristic polynomial of A, 42 diameter of U , 206 distance in a metric space Jacobian of a differentiable mapping f at x center subspace of a matrix, 44 (un)stable subspace of a matrix,

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 ... Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Qi Jianming 1,3 , Li Yezhou 2 and Yuan Wenjun ∗3 1 Department of Mathematics and ... 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 a

Ngày tải lên: 20/06/2014, 20:20

... t ≥ s, and the zero solution of (8) is stable Thus, the zero solution of (8) is asymptotically stable, and hence the zero solution of (1) is asymptotically stable The proof is complete □ Remark ... 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)

Ngày tải lên: 20/06/2014, 22:20

... 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 ... School of Science, University of Jinan, Jinan 250022, Shandong, PR China Full list of author information is available at the end of the article Abstract In this article, we study the existence of ... 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+ u(t) = f (t, v(t)), < t

Ngày tải lên: 21/06/2014, 03:20

... 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 ... differential equations by extending the idea of 17, 18 This method leads to computable and efficient solutions to linear and nonlinear operator equations The corresponding solutions of the integer-order equations ... introduces a new version of homotopy perturbation method for the solution of system of fractional-order differential equations In this approach, the solution is considered as a Taylor series expansion

Ngày tải lên: 21/06/2014, 05:20

... 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 ... Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Qi Jianming 1,3 , Li Yezhou 2 and Yuan Wenjun ∗3 1 Department of Mathematics and ... 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 a

Ngày tải lên: 21/06/2014, 17:20

... that uȷ is a solution of (1) if it is both a lower and an upper solution A solution u∗ in A ⊂ S is a maximal solution in the set A if u∗ ≥ u for any other solution u ∈ A The minimal solution in ... Distribution of the zeros of the solutions of hyperbolic differential equations with maxima Rocky Mt J Math 37(4) (2007) 1271–1281 12 Otrocol, D, Rus, IA: Functional differential equations with maxima of ... problem (1) has a maximal solution, u∗ , and a minimal one, u∗ , in [γ, λ]S Proof We shall prove the existence of the maximal solution since the existence of the minimal solution follows from the

Ngày tải lên: 21/06/2014, 17:20

... BOUNDARY VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS (5390) The Minh Tran 1. Solution a) Because '' u (x) 1 = , so we have the genaral form of u(x) : ( ) 2 x u ... separate var iableby dividing both sides of (1) by x G(t) dG t 1 1 d sin5x G dt dx G We can not solve by the method of separation of var iables because the presence of a terms like sin5x is forbidden ... see two solutions from the above are the same 2. ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 u u a ) sin5x t x We assum that u(x,t) x G t where x is only a function of x and G t is a function of t We

Ngày tải lên: 02/11/2014, 13:00