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[MUG] Re: Airy's Equation
| [MUG] Re: Airy's Equation |
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Author: Maple Group
Posted: 11/12/2000 14:47:16 GMT
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Subject: Airy's Equation
Use the expansions given in Abramowitz and Stegun, Handbook of
Mathematical Functions, Section 10.4.
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Chris Eilbeck email: "chris"
Department of Mathematics, Fax: +44 (0)131 451 3249
Heriot-Watt University, Phone: +44 (0)131 451 3220
Edinburgh EH14 4AS, Scotland. WWW: http://www.ma.hw.ac.uk/~chris/
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Date: Fri, 08 Dec 2000 10:42:58 -0500
From: Bill Bauldry "BauldryWC"
Subject: Airy's Equation
To: "maple-list"
Chuck,
A naive approach will work here to get one solution:
> de := (D@@2)(y)(x) - x*y(x) =0;
(2)
de := (D )(y)(x) - x y(x) = 0
> Order := 10: # if you want more than 5 terms
> dsolve(de, y(x), series);
3 4
y(x) = y(0) + D(y)(0) x + 1/6 y(0) x + 1/12 D(y)(0) x +
6 7 9 10
1/180 y(0) x + 1/504 D(y)(0) x + 1/12960 y(0) x + O(x )
But it may be more fun to work with the predefined functions:
> Order := 6:
> taylor(AiryAi(x), x);
> taylor(AiryBi(x), x);
(1/3) (1/6) (1/3)
3 3 GAMMA(2/3) 3 3
1/3 ---------- - 1/2 ----------------- x + 1/18 ---------- x -
GAMMA(2/3) Pi GAMMA(2/3)
(1/6)
3 GAMMA(2/3) 4 6
1/24 ----------------- x + O(x )
Pi
(5/6) (2/3) (5/6)
3 3 GAMMA(2/3) 3 3
1/3 ---------- + 1/2 ----------------- x + 1/18 ---------- x +
GAMMA(2/3) Pi GAMMA(2/3)
(2/3)
3 GAMMA(2/3) 4 6
1/24 ----------------- x + O(x )
Pi
Have fun ...
Regards,
Bill
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