systems of differential equations patrickjmt
Tài liệu Đề tài " Isomonodromy transformations of linear systems of difference equations" pptx
Ngày tải lên :
14/02/2014, 17:20
... equal
to I. The proof of uniqueness is complete.
To prove the existence we note, first of all, that it suffices to provide a
proof if one of the κ
i
’s is equal to ±1 and one of the δ
j
’s is equal ... solutions of
isomonodromy problems for such systems of difference equations. In the case
of one-interval gap probability this has been done (in a different language) in
[Bor], [BB]. One example of the ... ALEXEI BORODIN
Most of the results of the present paper can be carried over to the case
of q-difference equations of the form Y (qz)=A(z)Y (z). The q-difference
Schlesinger equations are, cf. (3)–(6),
(3q)
(4q)
(5q)
(6q)
B
i
(...
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Tài liệu Integration of Ordinary Differential Equations part 1 doc
Ngày tải lên :
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. ... 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, having ... 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 Press).
16.1...
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Tài liệu Integration of Ordinary Differential Equations part 2 pptx
Ngày tải lên :
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 Press).
16.1 ... 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
Ngày tải lên :
24/12/2013, 12:16
... generally useful stepper
routine is this: One of the arguments of the routine will of course be the vector of
dependent variables at the beginning of a proposed step. Call that y[1 n].Let
us require ... ,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
Ngày tải lên :
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 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
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 ... ordinary differential equations with minimal computational effort. (A possible
exception, infrequently encountered in practice, is discussed in §16.7.)
726
Chapter 16. Integration of Ordinary Differential...
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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 first-order equations, as discussed ... 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 systems...
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Tài liệu Integration of Ordinary Differential Equations part 7 pptx
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 ... nice feature of implicit methods holds only
for linear systems, but even in the general case implicit methods give better stability.
742
Chapter 16. Integration of Ordinary Differential Equations
Sample ... 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...
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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 ... 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...
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Enclosing solutions of systems of equations
Ngày tải lên :
12/01/2014, 22:20
... figure is reduced for the visualization.
Enclosing solutions of systems of equations
involving ODE
Aurelien Lejeune
National Institute of Informatics
2-1-2 Hitotsubashi, Chyoda-ku
Tokyo 101-8430 ... part.
Mots-clefs : syst`emes hybrides, equations differentielles ordinaires, anal-
yse par intervalles.
References
1. Hansen, E. and Sengupta, S.: Bounding solutions of systems of equations using
interval analysis. ... Solving of Hybrid
Constraint Systems. 3rd IFAC Conference on Analysis and Design of Hybrid Systems
(ADHS’09) (to appear)
10. K¨uhn, W.: Rigorously Computed Orbits of Dynamical Systems Without the Wrap-
ping...
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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
∈ ... context of derivative pricing.
The book does not claim to be a complete account of the state of the
art of the subject. Rather it attempts to provide a systematic framework for
an understanding of ... order of strong convergence from γ =0.5toγ =1.0. Nonethe-
less, the order of weak convergence of the Milstein scheme equals β =1.0,
which is not an improvement over the order of weak convergence of...
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Báo cáo "On the asymptotic behavior of delay differential equations and its relationship with C0 - semigoup " potx
Ngày tải lên :
22/03/2014, 11:20
... equivalence of systems of differential equations, Results of mathematic science 40
(1985) 245 (Russian).
[4] M. Svec, Itegral and asymptotic equivelence of two systems of diffrential equations, ... Journal of Science, Mathematics - Physics 23 (2007) 63-69
2. Main results
2.1. The uniformly stable of null solution of delay differential equations
Let us consider the delay differential equations
dx(t)
dt
= ... conditions of stable and asymptotic
equivalence (see [1-5]) of linear delay differential equations under nonlinear perturbation in Banach
space. The obtained results thank to use of the theories of general...
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galois theory of linear differential equations - m. van der put, m. singer
Ngày tải lên :
31/03/2014, 15:56
... translates into Z
L
=(r
a,b
)G
L
. A proof of Lemma 1.29 finishes
the proof of the theorem. ✷
Proof of lemma 1.29.
The proof is rather similar to the one of lemma 1.23. The only thing that we
have ... O-submodules N
1
,N
2
of N with N = N
1
⊕N
2
and N
i
= F
i
for i =1, 2.
Proof. The proof is similar to the proof of Proposition 3.17. Let S
1
and S
2
be the set of eigenvalues of E acting on F
1
and ... as a group of matrices
and has the structure of a linear algebraic group, that is, it is a group of invertible
matrices defined by the vanishing of a set of polynomials on the entries of these
matrices....
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