differential equations class 12 pdf
Tài liệu Integration of Ordinary Differential Equations part 5 pdf
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24/12/2013, 12:16
... Ordinary Differential Equations
(Englewood
Cliffs, NJ: Prentice-Hall),
Đ
6.1.4.
Stoer, J., and Bulirsch, R. 1980,
Introduction to Numerical Analysis
(New York: Springer-Verlag),
Đ
7.2 .12.
16.4 ... Method
The techniques described in this section are not for differential equations
containing nonsmooth functions. For example, you might have a differential
equation whose right-handside involves a ... quick-and-dirty, low-accuracy solution
of a set of equations. A second warning is that the techniques in this section are
not particularly good for differential equations that have singular points inside...
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Tài liệu Integration of Ordinary Differential Equations part 6 pdf
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... 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 ... is
a particular class of equations that occurs quite frequently in practice where you can gain
about a factor of two in efficiency by differencing the equations directly. The equations are
second-order ... KMAXX =12in bsstep.
CITED REFERENCES AND FURTHER READING:
Deuflhard, P. 1985,
SIAM Review
, vol. 27, pp. 505–535.
16.6 Stiff Sets of Equations
As soon as one deals with more than one first-order differential...
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Tài liệu Integration of Ordinary Differential Equations part 8 pdf
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... 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 ... REFERENCES AND FURTHER READING:
Gear, C.W. 1971,
Numerical Initial Value Problems in Ordinary Differential Equations
(Englewood
Cliffs, NJ: Prentice-Hall). [1]
Kaps, P., and Rentrop, P. 1979,
Numerische ... Predictor-corrector methods have been, we think, squeezed
752
Chapter 16. Integration of Ordinary Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...
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Tài liệu Solution of Linear Algebraic Equations part 12 pdf
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... matrices
a
11
a
12
a
21
a
22
and
c
11
c
12
c
21
c
22
(2.11.5)
are inverses of each other. Then the c’s can be obtained from the a’s by the following
operations (compare equations 2.7.22 ... 2.7.22 and 2.7.25):
R
1
= Inverse(a
11
)
R
2
= a
21
ì R
1
R
3
= R
1
ì a
12
R
4
= a
21
ì R
3
R
5
= R
4
a
22
R
6
= Inverse(R
5
)
c
12
= R
3
ì R
6
c
21
= R
6
ì R
2
R
7
= R
3
ì c
21
c
11
= R
1
R
7
c
22
= ... 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...
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Báo cáo hóa học: "OSCILLATION AND NONOSCILLATION THEOREMS FOR A CLASS OF EVEN-ORDER QUASILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS" pdf
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22/06/2014, 21:20
... solutions of (4.4).
OSCILLATION AND NONOSCILLATION THEOREMS
FOR A CLASS OF EVEN-ORDER QUASILINEAR
FUNCTIONAL DIFFERENTIAL EQUATIONS
JELENA MANOJLOVI
´
C AND TOMOYUKI TANIGAWA
Received 13 November ... Inequalities and Applications
Volume 2006, Article ID 4 2120 , Pages 1–22
DOI 10.1155/JIA/2006/4 2120
8 Quasilinear functional differential equations
Case 2. Let j
∈{0,1, ,n − 1} and suppose that ... theorems for a class of fourth order quasilinear func-
tional differential equations, Hiroshima Mathematical Journal 33 (2003), no. 3, 297–316.
[7]
, Oscillation criteria for a class of higher...
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Tài liệu Numerical Solution of Stochastic Differential Equations with Jumps in Finance pdf
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... Exercises . . . . . 504
12 Regular Weak Taylor Approximations 507
12. 1 Weak Taylor Schemes . . 507
12. 2 Commutativity Conditions. . 514
12. 3 Convergence Results . . . 517
12. 4 Exercises . . . . ... Sydney
PO Box 123
Broadway NSW 2007
Australia
eckhard.platen@uts.edu.au
Managing Editors
Boris Rozovski
˘
ı
Division of Applied Mathematics
Brown University
182 George St
Providence, RI 02 912
USA
rozovsky@dam.brown.edu
Geoffrey ... 978-3-642 -120 57-2
e-ISBN 978-3-642-13694-8
DOI 10.1007/978-3-642-13694-8
Springer Heidelberg Dordrecht London New York
Library of Congress Control Number: 2010931518
Mathematics Subject Classication...
- 868
- 1.3K
- 0
Báo cáo toán học: " Lyapunov-type inequalities for a class of even-order differential equations" doc
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... formatted
PDF and full text (HTML) versions will be made available soon.
Lyapunov-type inequalities for a class of even-order differential equations
Journal of Inequalities and Applications 2 012, 2 012: 5 ... differential equations.
Commun. Pure Appl. Anal. 11(2), 465–473 (2 012)
[19] Almansi, E: Sopra una delle esperienze di Plateau (Russian). Ann. Mat. Pura. Appl.
12, 1–17 (1905)
11
This Provisional PDF ... doi:10.1186/1029-242X-2 012- 5
Qi-Ming Zhang (zhqm20082008@sina.com)
Xiaofei He (hexiaofei525@sina.com)
ISSN 1029-242X
Article type Research
Submission date 19 October 2011
Acceptance date 12 January 2 012
Publication...
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Báo cáo hoa học: " Research Article On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay" pdf
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... pages
doi:10.1155/2010/143298
Research Article
On Connection between Second-Order Delay
Differential Equations and Integrodifferential
Equations with Delay
Leonid Berezansky,
1
Josef Dibl
´
ık,
2, 3
and Zden
˘
ek
ˇ
Smarda
3
1
Department ... differential equations with
damping described by 1.1.
Despite the obvious importance in applications, there are only few papers on delay
differential equations with damping.
4 Advances in Difference Equations
a2 ... Difference Equations, vol. 2009, Article ID 671625, 15
pages, 2009.
7 N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Functional
Differential Equations: ...
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Báo cáo hóa học: " Research Article A Generalized Wirtinger’s Inequality with Applications to a Class of Ordinary Differential Equations" docx
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... differential equations, ” Journal of Differential
Equations, vol. 189, no. 2, pp. 396–411, 2003.
2 R. D. Nussbaum, “A Hopf global bifurcation theorem for retarded functional differential equations, ”
Transactions ... several delays,” Journal of
Differential Equations, vol. 222, no. 2, pp. 425–438, 2006.
12 G. Fei, “Multiple periodic solutions of differential delay equations via Hamiltonian systems—I,”
Nonlinear ... one-dimensional differential-delay equations, ”
Tohoku Mathematical Journal, vol. 30, no. 1, pp. 13–35, 1978.
7 S. Chapin, “Periodic solutions of differential-delay equations with more than one delay,”...
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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
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22/06/2014, 18:20
... differential equations and some related perturbation results,” Annales Academiæ
Scientiarium Fennicæ. Mathematica, vol. 27, no. 2, pp. 273–290, 2002.
[9] E. Ince, Ordinary Differential Equations, ... Mathe-
matical Society, vol. 21, no. 2, pp. 334–360, 1970.
[12] S. A. Gao, Z. X. Chen, and T. W. Chen, The Complex Osc illation Theory of Linear Differential
Equations, Middle China University of Technology ... = e
z/q
.
Remark 4.3. Wiman-Valiron theory and its applications to differential equations (see [1,
pages 5-6] or [12, pages 71-72]).
Consider the linear differential equation
a
k
f
(k)
+ a
k−1
f
(k−1)
+...
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Báo cáo hóa học: " Research Article Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments" pdf
Ngày tải lên :
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... functional-differential
equations, ” Computers & Mathematic s with Applications, vol. 38, no. 11 -12, pp. 1–11, 1999.
[4] D. D. Ba
˘
ınov and D. P. Mishev, Osc illation Theory for Neutral Differential Equations ... neutral differential equations, ” Dynamic Sys-
tems and Applications, vol. 9, no. 3, pp. 353–360, 2000.
[23] P. Wang and W. Shi, “Oscillatory theorems of a class of even-order neutral equations, ” Applied
Mathematics ... 0
eventually for i
= 0,1, ,n − 1. Now, using (2 .12) weget
w
(n)
(t) −
b
a
w(t + τ − s)
1+α
d
s
q
1
(t,s) −
d
c
w(t + τ + s)
1+α
d
s
q
2
(t,s) ≥ 0. (2.14)
12 Journal of Inequalities and Applications
where...
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Báo cáo hóa học: "RELIABILITY OF DIFFERENCE ANALOGUES TO PRESERVE STABILITY PROPERTIES OF STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS" pdf
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... equivalent to the system of the
equations
2βp
12
=−1,
p
11
+ αp
12
+ βp
22
= 0,
2p
12
+
2α + σ
2
p
22
=−1,
(2.14)
with the solution
p
11
=
α
2β
−
1 −β
2α + σ
2
, p
12
=−
1
2β
, p
22
=
1 −β
β
2α ... the system of equations
B
2
d
22
−d
11
= 0,
B
d
12
+ Ad
22
−
d
12
= 0,
d
11
+2Ad
12
+ A
2
d
22
−d
22
=−1.
(3.18)
The solution of system (3.18)hastheform
d
11
= B
2
d
22
,
d
12
=
AB
1 −B
d
22
,
d
22
=
1+B
1 ... Ad
22
B
d
12
+ Ad
22
d
11
+2Ad
12
+ A
2
d
22
. (3.17)
RELIABILITY OF DIFFERENCE ANALOGUES TO PRESERVE
STABILITY PROPERTIES OF STOCHASTIC VOLTERRA
INTEGRO -DIFFERENTIAL EQUATIONS
LEONID...
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