system of nonlinear differential equations calculator
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
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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 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 Đ16.7.)
726
Chapter 16. Integration of Ordinary Differential...
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Tài liệu Integration of Ordinary Differential Equations part 6 pdf
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24/12/2013, 12:16
... 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 ... compatibility with bsstep the arrays y and d2y are of length 2n for a
system of n second-order equations. The values of y arestoredinthefirstnelements of y,
while the first derivatives are stored in...
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Tài liệu Integration of Ordinary Differential Equations part 7 pptx
Ngày tải lên :
24/12/2013, 12:16
... compatibility with bsstep the arrays y and d2y are of length 2n for a
system of n second-order equations. The values of y arestoredinthefirstnelements of y,
while the first derivatives are stored in ... 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 ... 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
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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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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, ... case
of linear delay differential equations under nonlinear perturbation (see [1, 13, 14]). Let’s consider the
two following differential equations:
dx(t)
dt
= Ax(t), t ≥ 0, (9)
VNU Journal of ... 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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Báo cáo toán học: " Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations" docx
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20/06/2014, 20:20
... made available soon.
Further results of the estimate of growth of entire solutions of some classes of
algebraic differential equations
Advances in Difference Equations 2012, 2012:6 doi:10.1186/1687-1847-2012-6
Oi ... ∈ (0, 1);
2. a sequence of complex numbers z
n
, |z
n
| < r;
Further results of the estimate of growth
of entire solutions of some classes of
algebraic differential equations
Qi Jianming
1,3
, ... complete.
17
[11] Gu, RM, Ding, JJ, Yuan, WJ: On the estimate of growth order of solutions of a
class of systems of algebraic differential equations with higher orders. J. Zhanjiang
Normal Univ. (in...
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Báo cáo hóa học: " Solving systems of nonlinear matrix equations involving Lipshitzian mappings" pdf
Ngày tải lên :
20/06/2014, 22:20
... classes of nonlinear matrix equations (see [8-21]). In this study, we consider
the following problem: Find (X
1
, X
2
, ,X
m
) ẻ (P(n))
m
solution to the following system
of nonlinear matrix equations:
X
r
i
i
= ... solving
different classes of systems of nonlinear matrix equations involving Lipshitzian
mappings.
2000 Mathematics Subject Classifications: 15A24; 65H05.
Keywords: nonlinear matrix equations, Lipshitzian ... for the
study of solutions to systems of nonlinear matrix equations involving contractive
mappings.
We first review the Thompson metric on the open convex cone P(n)(n ≥ 2), the set
of all nìn Hermitian...
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Báo cáo hóa học: " New criteria for stability of neutral differential equations with variable delays by fixed points method" docx
Ngày tải lên :
20/06/2014, 22:20
... neutral nonlinear differential equations with delay.
Nonlinear Anal. 74(12):3926–3933 (2011). doi:10.1016/j.na.2011.02.029
17. Raffoul, YN: Stability in neutral nonlinear differential equations ... asymptotic stability of the non-
linear impulsive stochastic differential equations and the impulsive stochastic partial
differential equations with infinite delays by means of the fixed point ... and stability in differential equations with variable delays. Nonlinear Anal. 63, e233–e242 (2005).
doi:10.1016/j.na.2005.02.081
11. Sakthivel, R, Luo, J: Asymptotic stability of nonlinear impulsive...
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