Tài liệu Integration of Ordinary Differential Equations part 6 pdf
Tài liệu Integration of Ordinary Differential Equations part 6 pdf
... 732
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 ... 505–535. [3]
16. 5 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,...
Tài liệu Integration of Ordinary Differential Equations part 5 pdf
... +H,whereHissupposed to be quite a large
7 26
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 ... using
¯
H
k
. The criterion of being “too small” is taken to be
H
k
α(k, q +1)<H ( 16. 4.15)
The α’s satisfy α(k, q +1) >α(k,q).
728
Chapter 16. Integration of...
Tài liệu Integration of Ordinary Differential Equations part 8 pdf
... methods have been, we think, squeezed
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 ... adjusting
the stepsize is difficult.
750
Chapter 16. Integration of Ordinary Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...
Tài liệu Integration of Ordinary Differential Equations part 1 doc
... America).
Chapter 16. 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 ... odeint
are drivers.
Section 16. 6 of this chapter treats the subject of stiff equations, relevant both to
ordinary differential equations and...
Tài liệu Integration of Ordinary Differential Equations part 2 pptx
... 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 Runge-Kutta ... 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...
Tài liệu Integration of Ordinary Differential Equations part 3 doc
... +2) are required. This accounts for the
7 16
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 ... a
2
h, y
n
+ b
21
k
1
)
···
k
6
=hf(x
n
+ a
6
h, y
n
+ b
61
k
1
+ ···+b
65
k
5
)
y
n+1
= y
n
+ c
1
k
1
+ c
2
k
2
+ c
3
k
3
+ c
4
k
4
+ c
5
k
5
+ c
6
k
6
+ O(h...
Tài liệu Integration of Ordinary Differential Equations part 4 ppt
... 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 ... usefulness ofthe modified midpointmethod tothe Bulirsch-Stoertechnique
(§ 16. 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 ......
Tài liệu Integration of Ordinary Differential Equations part 7 pptx
... 6. 02015272 865
#define C32 0.15975 068 467 3
#define C41 -1.8 563 4 361 867 7
#define C42 -8.50538085819
#define C43 -2.0840751 360 2
#define B1 3.9575037 466 3
#define B2 4 .62 4892388 36
#define B3 0 .61 7477 263 873
#define ... v(0) = 0 ( 16. 6.2)
By means of the transformation
u =2y−zv=−y+z ( 16. 6.3)
we find the solution
u =2e
−x
−e
−1000x
v = −e
−x
+ e
−1000x
( 16. 6.4)
If we integ...
Tài liệu Solution of Linear Algebraic Equations part 3 pdf
... Sciences
(New York:
McGraw-Hill), Program B-2, p. 298.
Westlake, J.R. 1 968 ,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New York: Wiley).
Ralston, A., and Rabinowitz, P. 1978,
A ... is called backsubstitution.Thecom-
bination of Gaussian elimination and backsubstitution yields a solution to the set
of equations.
The advantage of Gaussian eliminat...
Tài liệu Solution of Linear Algebraic Equations part 12 pdf
... R
1
× a
12
R
4
= a
21
× R
3
R
5
= R
4
− a
22
R
6
= Inverse(R
5
)
c
12
= R
3
× R
6
c
21
= R
6
× R
2
R
7
= R
3
× c
21
c
11
= R
1
− R
7
c
22
= −R
6
(2.11 .6)
... 5.3, 12 .6. [2]
2.11 Is Matrix Inversion an N
3
Process?
We close this chapter with a little entertainment, a bit of algorithmic prestidig-
itation which probes more deeply into the subject of matrix ... (outside North Ame...
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