zeroj.m

matlab的数学物理方程数值算法源程序。这是"Numerical Methods for Physics"第二版的matlab源程序。

function z = zeroj(m_order,n_zero)
% Zeros of the Bessel function J(x)
% Inputs
%   m_order = Order of the Bessel function
%   n_zero  = Index of the zero (first, second, etc.)
% Output
%   z = The "n_zero th" zero of the Bessel function

%* Use asymtotic formula for initial guess
beta = (n_zero + 0.5*m_order - 0.25)*pi;
mu = 4*m_order^2;
z = beta - (mu-1)/(8*beta) - 4*(mu-1)*(7*mu-31)/(3*(8*beta)^3);

%* Use Newton's method to locate the root
for i=1:5
  jj = bess(m_order+1,z);          
  % Use the recursion relation to evaluate derivative
  deriv = -jj(m_order+2) + m_order/z * jj(m_order+1);
  z = z - jj(m_order+1)/deriv;  % Newton's root finding  
end
return;