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# How to solve and plot the equation contain Bessel function

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Jun Xiao on 16 Mar 2020
Answered: Walter Roberson on 16 Mar 2020
I tried to use matlab to solve the equation which contain two different Bessel function and plot them, but I cannot solve it, even I used vpasolve or solve command, does anyone can help me with this? And what if I want to calculate the equation which need to differentiate some Bessel functions?
clc; clear all; close all;
syms a
n2 = 1:0.001:1.44;
n1 = 1.445;
y = n2/n1;
d = y.^2+1;
for n3 = 1000:1440
a1 = (((n3*0.001)./n1).^2+1)*besselj(1,a);
b1 = (a*besselj(2,a));
c1= a1-b1==0;
d = solve(c1,a);
end
plot(d,y,'b')
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### Answers (1)

Walter Roberson on 16 Mar 2020
syms a
n2 = 1:0.001:1.44;
n1 = 1.445;
y = n2/n1;
d = y.^2+1;
for n3 = 1000:1440
a1 = (((n3*0.001)./n1).^2+1)*besselj(1,a);
b1 = (a*besselj(2,a));
c1= a1-b1==0;
d(n3-1000+1) = vpasolve(c1,a);
end
plot(n1, d, 'b')
However, you will find that the solution is a constant 0. Besselj have zeros at 0, so making a = 0 gives you both sides equal to 0, which is an equality.
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