Numerical Methods for Ordinary Dierential Equations Episode 7 potx
Numerical Methods for Ordinary Dierential Equations Episode 7 potx
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Numerical Methods for Ordinary Dierential Equations Episode 1 docx
... methods 373
501 Transformations of methods 375
502 Runge–Kutta methods as general linear methods 376
503 Linear multistep methods as general linear methods 377
504 Some known unconventional methods ... 3 67
462 Variable stepsize for Nordsieck methods 371
463 Local error estimation 372
5 General Linear Methods 373
50 Representing Methods in General Linear Form 373...
Numerical Methods for Ordinary Dierential Equations Episode 2 docx
... these
assumptions, the equations of motion become
38 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS
13 Difference Equation Problems
130 Introduction to difference equations
While differential equations ... were
(y
1
,y
2
,y
3
,y
4
,y
5
,y
6
)=(0.994, 0, 0, 0, −2.001585106 379 0825224, 0) and the
period was 17. 0652165601 579 6.
34 NUMERICAL METHODS FOR ORDINARY DIF...
Numerical Methods for Ordinary Dierential Equations Episode 3 pot
... three stepsizes we have used, the errors are respectively
1 .72 474 5 − 1.6 875 55 = 0.0 371 90, 1 .72 474 5 − 1 .70 6 570 = 0.018 175 and
1 .72 474 5 −1 .71 576 0 = 0.008985. These error values approximately drop by ... 0.018 174 89 −0.0 173 7 078 47
20 0.00898483 −0.00 878 393 80
40 0.0044 670 4 −0.00441680 149
80 0.0022 272 1 −0.00221462 240
160 0.00111203 −0.00110889 480
320 0.00055562 −...
Numerical Methods for Ordinary Dierential Equations Episode 4 doc
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2
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Numerical Methods for Ordinary Dierential Equations Episode 5 docx
... 10
−5
4 .78 350
1 37
8
−10
2.15123 × 10
−6
4 .75 845
228
8
−11
4.53436 × 10
7
4 .74 429
382
8
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9. 575 67 × 10
−8
4 .73 529
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2.01165 × 10
−8
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1 078
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4 .75 7 37
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committed ... labelled by
Numerical Methods for Ordinary Differential Equations, Second Edition. J. C. Butcher
© 2008 John Wiley & Sons, Ltd. ISBN: 978 -0- 470 -72 335 -7...
Numerical Methods for Ordinary Dierential Equations Episode 6 ppsx
... manner:
0
1
4
1
4
1
4
1
8
1
8
1
2
00
1
2
3
4
3
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3
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8
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6
7
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12
7
8
7
7
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0
16
45
2
15
16
45
7
90
.
166 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS
Another approach would be to assume ... =
1
p!
. (324h)
170 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS
32 Low Order Explicit Methods
320 Methods of orders less than 4...
Numerical Methods for Ordinary Dierential Equations Episode 8 ppsx
... +
3
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99
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3
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51480
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For convenience, ... y
n
and y
n−1
from (357f) and (357g) and rearrange to deduce (357e).
234 NUMERICAL METHODS FOR ORDINARY DIFFE...
Numerical Methods for Ordinary Dierential Equations Episode 9 ppsx
... 4601448λ
10
− 72 571 68λ
9
+ 6842853λ
8
−418 176 0λ
7
+ 172 4256λ
6
−4 872 96λ
5
+94 176 λ
4
−12192λ
3
+1008λ
2
−48λ+1.
37 Symplectic Runge–Kutta Methods
370 Maintaining quadratic invariants
We recall Definition 357B ... +
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3
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5
8
ξ
4
−
1
20
ξ
5
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21
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3
+
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24
ξ
4
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7
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ξ
5
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ξ
7
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28
3
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+...
Numerical Methods for Ordinary Dierential Equations Episode 10 pot
... requirements.
Numerical Methods for Ordinary Differential Equations, Second Edition. J. C. Butcher
© 2008 John Wiley & Sons, Ltd. ISBN: 978 -0- 470 -72 335 -7
332 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL ... 1)
3
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