7/26/2019 Application of Bessel Function
1/15
Welcome
7/26/2019 Application of Bessel Function
2/15
contents
Bessel function and its application
Bessel functions of rst kind
Solutions using bessels functions ofrst kind(problem)
7/26/2019 Application of Bessel Function
3/15
7/26/2019 Application of Bessel Function
4/15
Applications of bessels
function Bessels euation arises %#en nding
seperable solutions to laplaceeuation and #elm#ot* euation insp#erical and cylindrical co+ordinates&
Bessels funtions are t#erefore
important for many problems of%a,e propagation and %a,epotentials&
7/26/2019 Application of Bessel Function
5/15
-or e'ample:
.ynamics of /oating bodies
0ngular resolution Heat conduction in cylindrical object
-reuency dependent friction in
circular pipelines& Bessels function also appear in signal
synt#esis (in fm or bessel lter)
7/26/2019 Application of Bessel Function
6/15
Bessels function
Bessel functions"rst dened by t#emat#ematician .aniel Bernoulli and t#engeneralised by -redric# Bessel"are t#e
canonical solutions y(') of bessels dierentialeuation
3y445'y45('3+n3)y 67 n7
%it# t#e general solution
96c;n( ')5c39n ') (
7/26/2019 Application of Bessel Function
7/15
7/26/2019 Application of Bessel Function
8/15
Solutions using bessels
function of first kind 0 circular plate ofunit radius #as itsplane insulated &if
t#e initialtemperature if -(=)and if t#e rim is kept
at temperature *ero"nd t#e temperatureof t#e plate at anytime&
1 =
7/26/2019 Application of Bessel Function
9/15
gi,en :if t#e initial temperature if -(=)and if t#e rim is kept at temperature *erot#e temperature of t#e plate at any time&
(="t)?@&
7/26/2019 Application of Bessel Function
10/15
7/26/2019 Application of Bessel Function
11/15
7/26/2019 Application of Bessel Function
12/15
A
7/26/2019 Application of Bessel Function
13/15
7/26/2019 Application of Bessel Function
14/15
7/26/2019 Application of Bessel Function
15/15
Thank you
Top Related