2. The table on the right gives the value of x(t 1) from numerical integration of the equation: Δt Euler d?x = -(2n)?x 0.005 1.103675 dt2 0.01 1.217707 using three different values of At, starting from the same initial value x(t = 0). The Euler scheme is used. 0.02 1.478699 (a) Write down the iteration steps explicitly. (b) Based on the results given, determine the order of accuracy.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2. The table on the right gives the value of x(t = 1) from
numerical integration of the equation:
At
Euler
d²x
= -(2n)?x
0.005
1.103675
dt2
0.01
1.217707
using three different values of At, starting from the same
initial value x(t = 0). The Euler scheme is used.
0.02
1.478699
(a) Write down the iteration steps explicitly.
(b) Based on the results given, determine the order of accuracy.
Transcribed Image Text:2. The table on the right gives the value of x(t = 1) from numerical integration of the equation: At Euler d²x = -(2n)?x 0.005 1.103675 dt2 0.01 1.217707 using three different values of At, starting from the same initial value x(t = 0). The Euler scheme is used. 0.02 1.478699 (a) Write down the iteration steps explicitly. (b) Based on the results given, determine the order of accuracy.
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