EDA365电子论坛网
标题:
贝塞尔函数零点的程序（转）
[打印本页]
作者:
House
时间:
2020-5-15 09:53
标题:
贝塞尔函数零点的程序（转）
+ y, k' u) _( V: v) t( H
函数参数 n：贝塞尔阶数 k：要求零点的个数 kind：第几类贝塞尔函数
8 }: W3 s3 Q/ E0 {# ^+ X3 D
* ]+ g4 \# z5 }+ P; b4 u+ o. {
function x=besselzero(n,k,kind)
: M" ]5 v8 h5 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% h( B: D( u" ]! T
%
, x0 C0 W W5 b
% besselzero.m
; W% C& x* y& Q4 J0 c% `
%
5 K( W2 `/ S2 p! w' e
% Find first k positive zeros of the Bessel function J(n,x) or Y(n,x)
$ a& W. V" V z C9 [
% using Halley's method.
! n0 O7 X1 k2 Q6 Y0 r$ D) A4 K
%
. c+ @# E9 V9 A( ^5 j. `
% Written by: Greg von Winckel - 01/25/05
: E: [- W+ K( R$ O! ~' U
% Contact: gregvw(at)chtm(dot)unm(dot)edu
) c8 V7 T- s5 Z
%
8 \% g1 k/ @4 b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@/ E7 y( e _* `
k3=3*k;
) c; j0 M5 @! t$ P9 d& ^2 A' e$ Y! G
x=zeros(k3,1);
- v9 n5 Z8 _& X5 h$ S7 g
for j=1:k3
3 S" p" f, n4 L
% W! x! u6 O, w$ m
% Initial guess of zeros
, O5 K3 y( W% E
x0=1+sqrt(2)+(j-1)*pi+n+n^0.4;
l+ S- ^$ w9 k; T! z' ^4 s
% X7 X: M9 s. ]" L
% Do Halley's method
$ z5 Z; _7 C" A+ S* r$ v* x
x(j)=findzero(n,x0,kind);
; m3 D( z2 A! y) c0 {0 c
if x(j)==inf
$ v5 W4 \* K# x
error('Bad guess.');
0 h# a6 G! s6 J7 S( y/ n' Y
end
9 s! K; z1 N! i6 J5 L, w6 N
. L2 A" y0 m1 O. K9 X( {4 J, f
end
$ z' I3 z( [( v% \' q# b
x=sort(x);
: _0 u7 U; b. v7 g% a8 A! o2 u+ k
dx=[1;abs(diff(x))];
$ Y: ^ q# U7 k8 _0 \! V1 |
x=x(dx>1e-8);
0 j3 s$ @ @" {6 O* |" P
x=x(1:k);
' p$ C/ M& w& Q9 C* o( P5 P6 n
function x=findzero(n,x0,kind)
. P1 H: t- s# t/ n6 B2 x
n1=n+1; n2=n*n;
/ W( d9 o. z$ D- ]& L
% Tolerance
: g# k$ P4 p, g( n( u8 F& _ o. e0 P
tol=1e-12;
) |: I& \/ }. @) y8 [2 t+ V) S! t1 `
% Maximum number of times to iterate
* M7 i4 v& d4 J o' C$ v
MAXIT=100;
7 Q0 y- S: c, K7 l& x' c% n
% Initial error
4 l5 T, _+ G' f8 I7 `2 ^
err=1;
# f- H7 _0 y- j* n/ }; ~) n: M" H3 j
iter=0;
+ |5 T" W0 ?/ X* l8 W. q
while abs(err)>tol & iter<MAXIT
/ \$ @6 H( u1 V
v/ D, C! \1 g
switch kind
6 W6 x9 c5 c, j7 c- L/ m- E
case 1
4 B9 K+ n+ w2 y+ m
a=besselj(n,x0);
/ f" ` Z+ D; Z( o9 A
b=besselj(n1,x0);
0 |# C. b! A. Y" S2 C
case 2
: V: J6 F$ e) b" W& R2 A
a=bessely(n,x0);
/ U' O+ f% G! X
b=bessely(n1,x0);
' t& c; |8 g; d
end
0 _+ y4 r# z" v* w f0 x
5 h: e9 d" `: h
x02=x0*x0;
4 u$ K- H. K0 `
Y: w4 u4 ?; J3 p; i5 o3 C
err=2*a*x0*(n*a-b*x0)/(2*b*b*x02-a*b*x0*(4*n+1)+(n*n1+x02)*a*a);
4 M1 Q) k, e2 x9 ^, D
! E/ K4 S' p, t- ?& y7 Z
x=x0-err;
. x/ e. d/ z9 K" O
x0=x;
! W. e# }. d% t a+ V; x
iter=iter+1;
3 `7 Z3 U" B) j! y2 j( V3 C' w {
. J: Q8 J6 O( Y3 r$ m
end
3 _8 w( K# j Z" \! b
if iter>MAXIT-1
* I7 ~5 ~ h6 M. s4 w8 k
warning('Failed to converge to within tolerance. ',...
0 |% [4 |4 ?. @ W/ m/ Z; r8 `
'Try a different initial guess');
( {; u9 n0 f5 A8 X$ U
x=inf;
8 z+ e3 F( R$ y
end
: v2 q3 `/ S; T
. a6 g, p; ~# A7 Z' G
作者:
naimei
时间:
2020-5-15 10:28
看看楼主的代码。
欢迎光临 EDA365电子论坛网 (https://bbs.eda365.com/)
Powered by Discuz! X3.2