Bessel Function Zeros The Bessel function of ordern, for n = 0, 1,2,..., can be defined by the definite integral √(x) = 1 * c Compute the first five positive roots J. (k=1,2,...,5), of the first six Bessel functions J₂(x), (n = 0, 1,..., 5). Script> 1 num_roots=5; num_functions=6; 2 %initial guess for roots (from Wolfram MathWorld) 3 zeros_guess=[2.4,3.8,5.1,6,7.5,8.7;... 4 5.5,7,8.4,9.7,11,12;... 5 8.6 10,11.6,13,14,16;... 6 11.8,13,15,16,18,19;... 7 15,16.4,18,19.4,21,22]; 8 %Compute first five roots of first six Bessel functions 9 %Put in variable bzeros with size (bzeros) = [5, 6] 10 11 12 13 14 %print table 15 fprintf('k 16 for k=1:num_roots 17 fprintf("%i',k) 18 19 20 21 22 23 end cos (xsin 0 - ne) do end J0(x) J1(x) J2(x) J3(x) J4(x) for n=0:num_functions-1 fprintf('%10.4f',bzeros(k,n+1)); fprintf('\n'); J5(x)\n') Save C Reset My Solutions > EE MATLAB Documentation ▶ Run Script ?
Bessel Function Zeros The Bessel function of ordern, for n = 0, 1,2,..., can be defined by the definite integral √(x) = 1 * c Compute the first five positive roots J. (k=1,2,...,5), of the first six Bessel functions J₂(x), (n = 0, 1,..., 5). Script> 1 num_roots=5; num_functions=6; 2 %initial guess for roots (from Wolfram MathWorld) 3 zeros_guess=[2.4,3.8,5.1,6,7.5,8.7;... 4 5.5,7,8.4,9.7,11,12;... 5 8.6 10,11.6,13,14,16;... 6 11.8,13,15,16,18,19;... 7 15,16.4,18,19.4,21,22]; 8 %Compute first five roots of first six Bessel functions 9 %Put in variable bzeros with size (bzeros) = [5, 6] 10 11 12 13 14 %print table 15 fprintf('k 16 for k=1:num_roots 17 fprintf("%i',k) 18 19 20 21 22 23 end cos (xsin 0 - ne) do end J0(x) J1(x) J2(x) J3(x) J4(x) for n=0:num_functions-1 fprintf('%10.4f',bzeros(k,n+1)); fprintf('\n'); J5(x)\n') Save C Reset My Solutions > EE MATLAB Documentation ▶ Run Script ?
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter2: Basic Linear Algebra
Section2.3: The Gauss-jordan Method For Solving Systems Of Linear Equations
Problem 9P
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Bessel Function Zeros
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![Bessel Function Zeros
The Bessel function of order n, for n = 0, 1,2, ..., can be defined by the definite integral
J₂(x)=1*cos (xsin 0 - no) do
Compute the first five positive roots jk (k=1,2,...,5), of the first six Bessel functions J₁(x), (n = 0, 1,..., 5).
Script
1 num_roots=5; num_functions=6;
2 %initial guess for roots (from Wolfram MathWorld)
3 zeros_guess=[2.4,3.8, 5.1,6,7.5,8.7;...
4
5.5,7,8.4,9.7,11,12;...
5
8.6 10,11.6,13,14,16;...
6 11.8,13,15, 16, 18, 19;...
7
15,16.4,18,19.4, 21, 22];
8 %Compute first five roots of first six Bessel functions
9 %Put in variable bzeros with size (bzeros) = [5, 6]
10
11
12
13
14 %print table
15 fprintf('k
16 for k=1:num roots
17
fprintf('%i',k)
18
19
20
21
22 end
23
for n=0:num_functions-1
end
JØ(x) J1(x) J2(x) J3(x) J4(x)
fprintf('%10.4f',bzeros(k,n+1));
fprintf('\n');
Assessment:
J5(x)\n')
Save C Reset
My Solutions >
MATLAB Documentation
▶ Run Script ?
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Transcribed Image Text:Bessel Function Zeros
The Bessel function of order n, for n = 0, 1,2, ..., can be defined by the definite integral
J₂(x)=1*cos (xsin 0 - no) do
Compute the first five positive roots jk (k=1,2,...,5), of the first six Bessel functions J₁(x), (n = 0, 1,..., 5).
Script
1 num_roots=5; num_functions=6;
2 %initial guess for roots (from Wolfram MathWorld)
3 zeros_guess=[2.4,3.8, 5.1,6,7.5,8.7;...
4
5.5,7,8.4,9.7,11,12;...
5
8.6 10,11.6,13,14,16;...
6 11.8,13,15, 16, 18, 19;...
7
15,16.4,18,19.4, 21, 22];
8 %Compute first five roots of first six Bessel functions
9 %Put in variable bzeros with size (bzeros) = [5, 6]
10
11
12
13
14 %print table
15 fprintf('k
16 for k=1:num roots
17
fprintf('%i',k)
18
19
20
21
22 end
23
for n=0:num_functions-1
end
JØ(x) J1(x) J2(x) J3(x) J4(x)
fprintf('%10.4f',bzeros(k,n+1));
fprintf('\n');
Assessment:
J5(x)\n')
Save C Reset
My Solutions >
MATLAB Documentation
▶ Run Script ?
Submit ?
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