Newton's Method
2013-10-26 8:00 am
The equation x + tanx = 0 is important in a variety of applications--- for example, in the study of the diffusion of heat. It has a sequence a1, a2, a3, ... of positive roots, with the nth root slightly larger than (n-0.5)π. Use Newton's method to compute a1 and a2 to three-place accuracy.
回答 (3)
2013-10-26 9:19 am
✔ 最佳答案
We wanted to solve f(x) = x + tan(x) = 0 using the Newton's method.First, we compute the derivative f'(x) = 1 + sec2(x).
Then we start the Newton's iteration by setting x0=2. Recall the Newton's iteration formula is xn=xn-1-f(x)/f(x0). We have
x0=2
x1=2.027314579
x2=2.028754298
x3=2.028757838
Therefore the first root, up to three place accuracy, is 2.029
For the second root, we do exactly the same thing starting with x0=5, so we haveWe have
x0=5
x1=4.879393859
x2=4.907699753
x3=4.91303811
x4=4.913180344
Therefore, the second root, up to three place accuracy, is 4.913.
2013-10-28 12:22 am
因為 Andrew 答得好。
2013-10-26 7:59 pm
Masterijk,點解贊助2點俾我既?^^
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