Michael P. answered • 05/05/16
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PhD - Applied Mathematician and Extraordinary Teacher
Mulan,
The variable k appears in two places in this equation. The iteration process (successive approximation) assumes (uses) a value for k in one of the places and then calculates the value for k in the other place with the equation.
The value of k that you have calculated should be better than the first value that you assumed (used) in the equation. So, use that recently calculated value and calculate a new value for k (in the same that you calculated the first value).
You should expect to get better and better values for k as you find the sequence of values calculated for k converging to a single value.
Hint: Rewrite your equation to make the calculations easier by placing one value of k by itself on one side of the equation:
k = (53.5458071/4)log(2k)
Hint: Start with some value of k other than zero!
Please let me know should you get stuck following these instructions. Thanks.
Michael.
Michael P.
You're welcome, Mulan.
The idea of iteration is to try one value for k, calculate another value for k, use that new value for k, calculate another value for k, over and aver again until the last two values in the sequence of ks are "really close".
Iteration is doing something (calculating k) over and over again.
In most cases (but not all) each newly calculated k is a more accurate answer. You can tell that the last few calculated values of k differ only in their last few digits. They become "really similar" ("really close").
You have to decide with which value of k to start and how many of the left most digits in the values of k should be identical before you stop the process (the iteration).
Starting with k = 1 was what I thought about starting with. (We think alike. :-))
I would expect that this problem as an example for students will quickly give a lot of similar digits after only a few steps. If your instructor did not explicitly say, I would stop after the first four or five digits in the values of k have become the same or after four or five steps (calculations).
Please let me know if you need more explanation. Thanks. And good luck!
Michael.
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05/06/16
Mulan H.
05/06/16