power series solution of differential equations pdf
Báo cáo hóa học: "OSCILLATION AND NONOSCILLATION THEOREMS FOR A CLASS OF EVEN-ORDER QUASILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS" pdf
Ngày tải lên :
22/06/2014, 21:20
... a solution of (A)belongingtoP(I
j
). This completes the
proof.
Unlike the solutions of class P(I) it seems to be very difficult (or impossible) to char-
acterize the existence of solutions of ... essential part of the proof of Lemma 4.4 has been proving the
existence of the solution for each of the integral equations (4.20), (4.21), and (4.22). That
has been done by the application of Schauder-Tychonoff ... differential equations
The objective of this paper is to study the oscillatory and nonoscillatory behavior of
solutions of (A). In Section 2 we begin with the classification of nonoscillatory solutions
of...
- 22
- 293
- 0
Báo cáo hóa học: "RELIABILITY OF DIFFERENCE ANALOGUES TO PRESERVE STABILITY PROPERTIES OF STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS" pdf
Ngày tải lên :
22/06/2014, 22:20
... illustrate some of our results with trajectories of (3.1). Note that in [30]anabsolute
correspondence of asymptotic mean square stability of the trivial solution and conver-
gence of trajectories ... equa-
tions, LMS Journal of Computation and Mathematics 6 (2003), 297–313.
[15] P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Applications
of Mathematics (New ... for asymptotic stability of the trivial solution
of (1.1).
We proceed in the following way to obtain asymptotic mean square stability conditions
for the trivial solution of (1.1) via Lyapunov’s...
- 22
- 275
- 0
Báo cáo hóa học: " Polynomial solutions of differential equations" ppt
Ngày tải lên :
20/06/2014, 22:20
... Advances in Difference Equations 2011, 2011:58
http://www.advancesindifferenceequations.com/content/2011/1/58
Page 3 of 12
RESEARCH Open Access
Polynomial solutions of differential equations
H Azad
*
, ... polynomial solutions of a class of linear differential equations of the second order. Bull A M S. 36,
77–84 (1930). doi:10.1090/S0002-9904-1930-04888-0
Azad et al. Advances in Difference Equations ... Correspondence:
hassanaz@kfupm.edu.sa
Department of Mathematics &
Statistics, King Fahd University of
Petroleum & Minerals, Dhahran,
Saudi Arabia
Abstract
A new approach for investigating polynomial solutions of differential equations...
- 12
- 425
- 0
Báo cáo hóa học: " Some new nonlinear integral inequalities and their applications in the qualitative analysis of differential equations" potx
Ngày tải lên :
21/06/2014, 01:20
... second example, we will obtain the
bound of the solutions of an integral equation.
For the sake of proving the global existence of solutions of differential equations, we
first recall some basic ... integral equation, differential equa-
tion, bounded
1 Introduction
During the past decades, with the development of the theory of differential and integral
equations, a lot of integral inequalities, ... discovered,
which play an important role in the research of boundedness, global existence, stability
of solutions of differential and integral equations.
In [9], the following two theorems for retarded...
- 15
- 430
- 0
Báo cáo hóa học: " Research Article Local Regularity Results for Minima of Anisotropic Functionals and Solutions of Anisotropic Equations" pdf
Ngày tải lên :
22/06/2014, 18:20
... 2.1.
4. Local solutions of anisotropic equations
In this section, we prove a local regularity result for weak solutions of anisotropic equations.
Let u ∈ W
1,q
i
loc
Ω be a local solution of the anisotropic ... conditions depending on u, in the proof of the local regularity
results, w e have to estimate the integral of some power of |u| by means of |Du|.Todothis,we
will make use of the Sobolev inequality that ... supported by Special Fund of Mathematics Research of Natural Science Foun-
dation of Hebei Province no. 07M003 and Doctoral Foundation of the Department of Edu-
cation of Hebei Province B2004103....
- 11
- 165
- 0
Tài liệu Numerical Solution of Stochastic Differential Equations with Jumps in Finance pdf
Ngày tải lên :
19/02/2014, 22:20
... collection of events, sigma-algebra
A
filtration
E(X) expectation of X
E(X |A) conditional expectation of X under A
P (A) probability of A
P (A |B) probability of A conditioned on B
∈ element of
∈ ... continuous solutions of SDEs. The discrete time approximation of
SDEs with jumps represents the focus of the monograph. The reader learns
about powerful numerical methods for the solution of SDEs with ... discusses powerful martingale representations and
variance reduction techniques in the context of derivative pricing.
The book does not claim to be a complete account of the state of the
art of the...
- 868
- 1.3K
- 0
Tài liệu Integration of Ordinary Differential Equations part 5 pdf
Ngày tải lên :
24/12/2013, 12:16
... extrapolate each
component of a vector of quantities.
728
Chapter 16. Integration of Ordinary Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... 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 ... 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...
- 9
- 486
- 0
Tài liệu Integration of Ordinary Differential Equations part 6 pdf
Ngày tải lên :
24/12/2013, 12:16
... 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 ... 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 rst-order equations, as discussed ... compatibility with bsstep the arrays y and d2y are of length 2n for a
system of n second-order equations. The values of y arestoredinthefirstnelements of y,
while the first derivatives are stored in...
- 3
- 395
- 0
Tài liệu Integration of Ordinary Differential Equations part 8 pdf
Ngày tải lên :
24/12/2013, 12:16
... Problems in Ordinary Differential Equations
(Englewood
Cliffs, NJ: Prentice-Hall), Chapter 9. [1]
Shampine, L.F., and Gordon, M.K. 1975,
Computer Solution of Ordinary Differential Equations.
The Initial ... adjusting
the stepsize is difficult.
748
Chapter 16. Integration of Ordinary Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... high-precision
solution of very smooth equations with very complicated right-hand sides, as we
will describe later.
Nevertheless, these methods have had a long historical run. Textbooks are
full of information...
- 6
- 457
- 0
Tài liệu Solution of Linear Algebraic Equations part 3 pdf
Ngày tải lên :
24/12/2013, 12:16
... is called backsubstitution.Thecom-
bination of Gaussian elimination and backsubstitution yields a solution to the set
of equations.
The advantage of Gaussian elimination and backsubstitutionover ... 42
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... York:
McGraw-Hill), Program B-2, p. 298.
Westlake, J.R. 1968,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New York: Wiley).
Ralston, A., and Rabinowitz, P. 1978,
A...
- 3
- 404
- 0
Tài liệu Solution of Linear Algebraic Equations part 12 pdf
Ngày tải lên :
24/12/2013, 12:16
... 104
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... submatrices. Imagine doing the inversionof a very large matrix, of order
N =2
m
, recursively by partitions in half. At each step, halving the order doubles
the number of inverse operations. But this ... complicated nature
of the recursive Strassen algorithm, you will find that LU decomposition is in no
immediate danger of becoming obsolete.
If, on the other hand, you like this kind of fun, then try...
- 3
- 312
- 0
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
... differential equations, ” Journal of Computational and Applied Mathematics, vol. 223, no.
1, pp. 438–448, 2009.
24 J. Yan, “Existence of positive periodic solutions of impulsive functional differential equations ... economics. The theory of impulsive differential equations has
become an important area of investigation in the recent years and is much richer than the
corresponding theory of differential equations. For ... 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...
- 15
- 372
- 0
Báo cáo hóa học: " Research Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument" ppt
Ngày tải lên :
21/06/2014, 20:20
... Spectrum of Almost Periodic Solution of
Second-Order Neutral Delay Differential Equations
with Piecewise Constant of Argument
Li Wang and Chuanyi Zhang
Department of Mathematics, Harbin Institute of ... is a solution of 1.1, then xtpxt − 1
are continuous at t ∈ R, which guarantees the uniqueness of solution of 1.1 and cannot be
omitted.
To study the spectrum of almost periodic solution ... one sees that if xt is a solution of 1.1 and |p|
/
1, then one
gets 2.3 and 2.4. In fact, a solution of 1.1 is constructed by the common solution {x
n
} of
2.3 and 2.4. Moreover,...
- 14
- 335
- 0
Báo cáo hóa học: " Research Article On Complex Oscillation Property of Solutions for Higher-Order Periodic Differential Equations Zong-Xuan Chen and Shi-An Gao" pdf
Ngày tải lên :
22/06/2014, 18:20
... that the a bove proof remains valid if we interchange the roles of G
j
and g
j
as at the end of the proof of Lemma 2.6.TheproofofTheorem 1.3 is completed.
4. Lemma for the proof of Theorem 1.6
Lemma ... hence every solution f
≡ 0of
(1.2) satisfies (1.14). This completes the proof of Theorem 1.6.
6. Proofs of corollaries
Proof of Corollary 1.4. By Remark 2.7, we see that the hypotheses of Theorem ... differential equation of the form (4.2) whose coeffi-
cients are analytic in a neighborhood of z
=∞andhaveatmostapoleatz =∞.
Proof of Lemma 4.1. Using a method similar to the proof of Lemma 2.6, combining...
- 13
- 317
- 0
Báo cáo hóa học: " Research Article Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments" pdf
Ngày tải lên :
22/06/2014, 18:20
... eventually positive solution of deg ree
0 whenever n is even.
Then every solution x(t) of (1.1)isoscillatory.
Proof. Suppose that there exists an eventually positive solution x(t )of( 1.1). Letting
y(t)
= ... positive solution of
degree n;
(b) equation (E
μ
k
)withμ = 1+α + β and k = τ has no eventually positive solution of
degree 0 whene ver n is even.
Then every solution x(t) of (1.1)isoscillatory.
Proof. ... Dahiya and A. Zafer 5
Having an eventually positive solution w of degree 0 of inequality (2.14) contradicts (c).
The proof is complete.
The proof of the next theorem is similar, and hence we omit...
- 13
- 201
- 0