nonlinear ordinary differential equations examples
Tài liệu Integration of Ordinary Differential Equations part 1 doc
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15/12/2013, 04:15
... Integration of Ordinary
Differential Equations
16.0 Introduction
Problems involving ordinary differential equations (ODEs) can always be
reduced to the study of sets of first-order differential equations. ... 1973,
Computational Methods in Ordinary Differential Equations
(New York: Wiley).
Lapidus, L., and Seinfeld, J. 1971,
Numerical Solution of Ordinary Differential Equations
(New
York: Academic ... auxiliary variables.
The generic problem in ordinary differential equations is thus reduced to the
study of a set of N coupled first-order differential equations for the functions
y
i
,i=1,2, ,N,...
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Tài liệu Integration of Ordinary Differential Equations part 2 pptx
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15/12/2013, 04:15
... 1973,
Computational Methods in Ordinary Differential Equations
(New York: Wiley).
Lapidus, L., and Seinfeld, J. 1971,
Numerical Solution of Ordinary Differential Equations
(New
York: Academic ... REFERENCES AND FURTHER READING:
Gear, C.W. 1971,
Numerical Initial Value Problems in Ordinary Differential Equations
(Englewood
Cliffs, NJ: Prentice-Hall).
Acton, F.S. 1970,
Numerical Methods ... 710
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 Integration of Ordinary Differential Equations part 3 doc
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... 722
Chapter 16. Integration of Ordinary Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... REFERENCES AND FURTHER READING:
Gear, C.W. 1971,
Numerical Initial Value Problems in Ordinary Differential Equations
(Englewood
Cliffs, NJ: Prentice-Hall). [1]
Cash, J.R., and Karp, A.H. 1990,
ACM ... ,n−1
y(x+H)≈y
n
≡
1
2
[z
n
+z
n−1
+hf(x + H, z
n
)]
(16.3.2)
714
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 Integration of Ordinary Differential Equations part 4 ppt
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24/12/2013, 12:16
... 722
Chapter 16. Integration of Ordinary Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... REFERENCES AND FURTHER READING:
Gear, C.W. 1971,
Numerical Initial Value Problems in Ordinary Differential Equations
(Englewood
Cliffs, NJ: Prentice-Hall). [1]
Cash, J.R., and Karp, A.H. 1990,
ACM ... ofthe modied midpointmethod tothe Bulirsch-Stoertechnique
(Đ16.4) derives from a deep result about equations (16.3.2), due to Gragg. It turns
out that the error of (16.3.2), expressed as a power...
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Tài liệu Integration of Ordinary Differential Equations part 5 pdf
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24/12/2013, 12:16
... solutions
to ordinary differential equations with minimal computational effort. (A possible
exception, infrequently encountered in practice, is discussed in Đ16.7.)
726
Chapter 16. Integration of Ordinary ... REFERENCES AND FURTHER READING:
Gear, C.W. 1971,
Numerical Initial Value Problems in Ordinary Differential Equations
(Englewood
Cliffs, NJ: Prentice-Hall),
Đ
6.1.4.
Stoer, J., and Bulirsch, R. ... 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...
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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 ... 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 ... reason for this is explained below). This is so even
732
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 Integration of Ordinary Differential Equations part 7 pptx
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... general case implicit methods give better stability.
742
Chapter 16. Integration of Ordinary Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... rule:
y
n+1
− y
n−1
=2hf
y
n+1
+ y
n−1
2
(16.6.29)
738
Chapter 16. Integration of Ordinary Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... 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...
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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 ... 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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ordinary differential equations and dynamical systems - g. teschl
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... manuscript provides an introduction to ordinary differential
equations and dynamical systems. We start with some simple examples
of explicitly solvable equations. Then we prove the fundamental ... the
Melnikov method for homoclinic orbits.
Keywords and phrases. Ordinary differential equations, dynamical systems,
Sturm-Liouville equations.
Typeset by A
M
S-L
A
T
E
X and Makeindex.
Version: ... conditions. Furthermore we consider linear equations,
the Floquet theorem, and the autonomous linear flow.
Then we establish the Frobenius method for linear equations in the com-
plex domain and investigates...
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an introduction to ordinary differential equations
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12/05/2014, 03:24
... a
systematic way.
3.1 Ordinary and partial differential equations
The most significant distinction is between ordinary and partial differential equa-
tions, and this depends on whether ordinary or partial ... Summary of phase portraits for linear equations 301
31.1 *Jordan canonical form 301
Exercises 305
Part VI Coupled nonlinear equations 307
32 Coupled nonlinear equations 309
32.1 Some comments on ... derivatives).
AN INTRODUCTION TO ORDINARY
DIFFERENTIAL EQUATIONS
This refreshing, introductory textbook covers standard techniques for solving ordi-
nary differential equations, as well as introducing...
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báo cáo hóa học: " Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type" doc
Ngày tải lên :
21/06/2014, 02:20
... order ordinary differential
equations. Math Inequal Appl. 6, 477–485 (2003)
23. Luo, ZG, Shen, JH, Nieto, JJ: Antiperiodic boundary value problem for first -order impulsive ordinary differential
equations. ... conditions for differ-
ential equations or impulsive differential equations. To the best of our knowledge it is
the first article to deal with integro -differential equations with “an ti-peri odic” ... 34D09,34D99.
Keywords: Boundary value problems, integro -differential equations, fixed-point
motheds
1. Introduction and preliminaries
As is known, integro -differential equations find many applications in various...
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