Bessel functions often arise in advanced engineering analyses such as the study of electric fields.x1.82.02.22.42.6 J1(x)0.58150.57670.55600.52020

Jaya Legge 2021-10-07 Answered

Bessel functions often arise in advanced engineering analyses such as the study of electric fields. Here are some selected values for the zero-order Bessel function of the first kind.
\(\begin{array}\\ x&1.8&2.0&2.2&2.4&2.6\\ J_1(x)&0.5815&0.5767&0.5560&0.5202&0.4708 \end{array}\)
Estimate \(J_1(2.1)\) using third- and fourth-order interpolating polynomials. Determine the percent relative error for each case based on the true value, which can be determined with MATLAB’s built-in function besselj.

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Expert Answer

Bertha Stark
Answered 2021-10-08 Author has 3460 answers
y = 0.5743, 0.56834, 0.56829, 0.5683
ea3 = 0.00081573
ea4 = 0.0020712
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Bessel functions often arise in advanced engineering and scientific analyses such as the study of electric fields. These functions are usually not amenable to straightforward evaluation and, therefore, are often compiled in standard mathematical tables.
\(\begin{array}\\ x&1.8&2.0&2.2&2.4&2.6\\ J_1(x)&0.5815&0.5767&0.5560&0.5202&0.4708 \end{array}\)
Estimate \(J_1(2.1)\), (a) using an interpolating polynomial and (b) using cubic splines. Note that the true value is 0.5683

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