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Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
book

Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition

by Harold Klee, Randal Allen
April 2016
Intermediate to advanced content levelIntermediate to advanced
815 pages
31h 29m
English
CRC Press
Content preview from Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
Fourth-order RK formulas are the most common of all the RK numerical integrators for reasons
we shall discuss shortly. The derivation is patterned after the approach used for the lower-order RK
methods. Flexibili ty in the choice of several parameters results in a family of RK-4 integrators.
A popular RK-4 integrator is illustrated in Figure 6.5.
The derivative function evaluations are computed according to
k
1
¼ f [t
i
, x
A
(i)], x
A
i þ
1
2

¼ x
A
(i) þ
T
2
k
1
(6:60)
k
2
¼ ft
iþ1=2
, x
A
i þ
1
2

,
^
x
A
i þ
1
2

¼ x
A
(i) þ
T
2
k
2
(6:61)
k
3
¼ ft
iþ1=2
,
^
x
A
i þ
1
2

,
^
x
A
(i þ 1) ¼ x
A
(i) þ Tk
3
(6:62)
k
4
¼ f [t
iþ1
,
^
x
A
(i þ 1)] (6:63)
and the updated state x
A
(i þ1) is obtained from
x
A
(i þ 1
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Publisher Resources

ISBN: 9781439836736