Numerical inversion of a general incomplete elliptic integral
نویسندگان
چکیده
منابع مشابه
Numerical inversion of a general incomplete elliptic integral
We present a numerical method to invert a general incomplete elliptic integral with respect to its argument and/or amplitude. The method obtains a solution by bisection accelerated by the half argument formulas and the addition theorems to evaluate the incomplete elliptic integrals and Jacobian elliptic functions required in the course. If a faster execution is desirable at the cost of complexi...
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The incomplete elliptic integral of the second kind, EðsinðTÞ;mÞ R T 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 m sinðT Þ q dT 0 where m 2 1⁄20;1 is the elliptic modulus, can be inverted with respect to angle T by solving the transcendental equation EðsinðTÞ;mÞ z 1⁄4 0. We show that Newton’s iteration, T 1⁄4 T EðsinðTÞ;mÞ z f g ffiffiffiffiffi...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2013
ISSN: 0377-0427
DOI: 10.1016/j.cam.2012.07.002