# Help for solving linear system that involves Bessel and Hankel Functions

2 views (last 30 days)

Show older comments

I have tried starting with the following but I don't know how to proceed. Also, I don' t know to do it for the case of M different of N.

First I am defining the Bessel and Hankel Functions and their derivatives:

M= 10;

N = M;

scaled = 1; % parameter for Bessel functions (to avoid overflow for large M)

for m = 0:M

J_c(m+1) = besselj(m,k*r,scaled);

H_s(m+1) = besselh(m,2,k*r,scaled);

J_cp(m+1) = m*(besselj(m,k*r,scaled))./(k_c*a_c) - (besselj(m+1,k*r,scaled));

H_sp(m+1) = (1/2)*(besselh(m-1,2,k*r,scaled)-besselh(m+1,2,k*r,scaled));

##### 0 Comments

### Answers (1)

Torsten
on 3 Jan 2024

Edited: Torsten
on 3 Jan 2024

What kind of functions are the P_m^n and Q_m^n ?

Fix a finite upper bound N for the loops instead of Inf. Then you have a linear system of equations in A_0,...,A_N,B_0,...,B_N. Set up the coefficient matrix Mat and the right-hand side vector rhs and solve it using \

Use 2*N as the new upper bound for the loops instead of Inf and check whether the solutions of your first computation (with N as upper bound) don't differ much from those of this computation.

Example for solving a linear system in MATLAB:

Mat = [1 3 ; 4 6];

rhs = [-2;5];

sol = Mat\rhs

##### 9 Comments

Torsten
on 18 Jan 2024

Edited: Torsten
on 18 Jan 2024

### See Also

### Categories

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!