examples of nonlinear ordinary differential equations
Tài liệu Integration of Ordinary Differential Equations part 1 doc
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... 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. ... 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, ... 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...
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Tài liệu Integration of Ordinary Differential Equations part 2 pptx
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... 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 ... 710
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 ... that derive from this basic
712
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...
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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 0-521-43108-5)
Copyright ... ,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 0-521-43108-5)
Copyright ... informationcan beobtained. Obviously,
720
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...
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Tài liệu Integration of Ordinary Differential Equations part 4 ppt
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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 0-521-43108-5)
Copyright ... Initial Value Problems in Ordinary Differential Equations
(Englewood
Cliffs, NJ: Prentice-Hall). [1]
Cash, J.R., and Karp, A.H. 1990,
ACM Transactions on Mathematical Software
, vol. 16, pp. 201–
222. ... modified midpoint method, which advances a vector
of dependent variables y(x) from a point x to a point x + H by a sequence of n
substeps each of size h,
h = H/n (16.3.1)
In principle, one could...
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Tài liệu Integration of Ordinary Differential Equations part 5 pdf
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... 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 ... differential equations. For n
k
subdivisions in H, the number of function evaluations can be found from the recurrence
A
1
= n
1
+1
A
k+1
= A
k
+ n
k+1
(16.4.6)
730
Chapter 16. Integration of Ordinary Differential...
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Tài liệu Integration of Ordinary Differential Equations part 6 pdf
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... 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 ... 734
Chapter 16. Integration of Ordinary Differential Equations
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Tài liệu Integration of Ordinary Differential Equations part 7 pptx
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... form of the midpoint 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 ... intermediate values of y and x.
y[i]=ysav[i]+A31*g1[i]+A32*g2[i];
736
Chapter 16. Integration of Ordinary Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... 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...
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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 ... 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 0-521-43108-5)
Copyright ... adjusting
the stepsize is difficult.
748
Chapter 16. Integration of Ordinary Differential Equations
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ordinary differential equations and dynamical systems - g. teschl
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... neighborhood of the singular point
z = 0 and we can now try to go the opposite way. Given a solution of the
system of linear equations (4.38), where α is an eigenvalue of A
0
we get a
solution of our ... block of A
0
. Or m
l
>
m
l−1
and (α + m
l
− A
0
)u
l,m
l
= 0, that is, α + m
l
is another eigenvalue of
A
0
.
So we have found a quite complete picture of the possible forms of solu-
tions of ... 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...
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an introduction to ordinary differential equations
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... Classification of differential equations 11
3.1 Ordinary and partial differential equations 11
3.2 The order of a differential equation 13
3.3 Linear and nonlinear 13
3.4 Different types of solution ... Preface
The aim of this book is to deal with all of the elementary methods for obtaining
explicit solutions of ordinary differential equations, and then to introduce the ideas
of qualitative analysis ... discussion of the issues of existence and uniqueness
of solutions, and treats the standard classes of first order differential equations
that can be solved explicitly, as well as covering exact equations...
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