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Question 1
Given the IVP shown in Example 4, find the first three iterations when then initial current -1 A. Use the value h = 0.1.
Answer: y1 = (-1.0, 0.5)T, y2 = (-0.95, 0.499500)T, y3 = (-0.90005, 0.479500)T.
Question 2
Given the IVP shown in Example 2, find the first three iterations when the forcing function is v(t) = e-t for t ≥ 0. Replace the cos(t) with the derivative of the new forcing function and use h = 0.1 and assume the system is initially at rest.
Answer: y1 = (0, -0.01)T, y2 = (-0.01, -0.11052)T, y3 = (-0.021052, -0.10652)T.
Question 3
Consider the circuit in Figure 1.
![](question01.png)
Figure 1. An RLL circuit.
From your circuits course, you can determine that the differential equation describing the current flowing across the second inductor is given by:
Rewrite this as a system of 1st-order differential equations.
Question 3
Given the 3rd-order IVP
y(0) = 3
y(1)(0) = 2
y(2)(0) = 1
Approximate y(1) by using one step of Euler's method and then again, by using 2 and then 4 steps of Euler's method.
Answer: (5, 3, 2)T; (4, 2.5, 1.5)T and (5.25, 3.25, 1.5)T; (3.5, 2.25, 1.25)T, (4.0625, 2.5625, 1.375)T, (4.703125, 2.90625, 1.40625)T, and (5.4296875, 3.2578125, 1.35546875)T.
Question 4
Given the 3rd-order IVP
y(0) = 3
y(1)(0) = 2
y(2)(0) = 1
Approximate y(1) by using one step of Euler's method and then again, by using 2 and then 4 steps of Euler's method.
Answer: (5, 3, 0)T; (4, 2.5, 0.5)T and (5.25, 2.75, 0.375)T; and (3.5 2.25 0.75)T, (4.0625 2.4375 0.578125)T, (4.671875 2.58203125 0.474609375)T, (5.3173828125 2.70068359375 0.42565917975)T.
Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.