systems of differential equations practice problems
Tài liệu Đề tài " Isomonodromy transformations of linear systems of difference equations" pptx
Ngày tải lên :
14/02/2014, 17:20
... 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 ... 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 ... 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 ... 708
Chapter 16. Integration of Ordinary Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
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Tài liệu Integration of Ordinary Differential Equations part 2 pptx
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15/12/2013, 04:15
... 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 ... 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 ... that derive from this basic
712
Chapter 16. Integration of Ordinary Differential Equations
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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 ... 1971,
Numerical 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, ... ,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
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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 ... 1971,
Numerical 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, ... 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
... 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 ... 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 ... 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 Differential...
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Tài liệu Integration of Ordinary Differential Equations part 6 pdf
Ngày tải lên :
24/12/2013, 12:16
... 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 ... 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 ... 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 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 ... 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)
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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
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24/12/2013, 12:16
... Value 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 ... 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)
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