5fceb06e-2bbf-415d-a37d-a18f8478c593 7 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

j 0201 range :

scale j j 0 * augment :

Z scale + 14 black plot :

F(x) = x * Bessel(1;x) - 1,01 * Bessel(0;x).

x F x 1 x Bessel * 1.01 0 x Bessel * - eval :

0 x Bessel 1 x Bessel 2 1 sys x F

x f x F eval 11 line :

Plot the unary intervals to help bracket Dichotomy

0 2 0 2 - 2 2 mat x f 0 0 + 14 black 1 0 + 14 black 2 0 + 14 black 3 0 + 14 black 4 0 + 14 black 5 0 + 14 black 6 0 + 14 black 7 0 + 14 black 8 0 + 14 black 9 0 + 14 black 10 0 + 14 black 11 0 + 14 black 12 0 + 14 black 13 0 + 14 black 14 0 + 14 black 15 0 + 14 black 16 0 + 14 black 17 0 + 14 black 18 0 + 14 black 19 0 + 14 black 20 0 + 14 black 21 5 mat 3 1 sys

a 1.25 : b 1.27 : 12 mat xn b a + (2 / : 21 line

ε 1014 -^:

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

.. sanity ..

xn 1.26063584661327

xn f 91015 -^*

iterates n 39

a 3.5 : b 4.5 : 12 mat xn b a + (2 / : 21 line

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

.. sanity ..

xn 4.08178816632211

xn f 41015 -^* -

iterates n 48

a 6.5 : b 7.5 : 12 mat xn b a + (2 / : 21 line

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

.. sanity ..

xn 7.15716948449889

xn f 51015 -^*

iterates n 51

a 10 : b 10.5 : 12 mat xn b a + (2 / : 21 line

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

.. sanity ..

xn 10.2719497005655

xn f 11014 -^*

iterates n 59

a 13 : b 14 : 12 mat xn b a + (2 / : 21 line

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

.. sanity ..

xn 13.3991396481971

xn f 41015 -^* -

iterates n 106

a 16 : b 17 : 12 mat xn b a + (2 / : 21 line

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

.. sanity ..

xn 16.5317616124364

xn f 41015 -^* -

iterates n 68

a 19 : b 20 : 12 mat xn b a + (2 / : 21 line

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

.. sanity ..

xn 19.6672349308422

roots 1.26063584661327 4.08178816632211 7.15716948449889 10.2719497005655 13.3991396481971 16.5317616124364 19.6672349308422 71 mat :

xn f 61016 -^*

iterates n 41