$u'(x_p)+g(x_p)u(x_p)=f(x_p)+ \frac{1}{2M} \sum_q^b K(x_p,t_q,U(t_q),u'(t_q)) $(20)
$P=1,2,....2M$$q=1,2,...2M;$
the jacobian of the system(20 is given as follows:
J(p,r) =\begin{cases}1+ \phi _1(p,p) & p = r\ \phi _1(p,r) & p \neq r\end{cases}
که در آن:
$ \phi _1(p,p)=g(x_p) \frac{ \delta u(x_p)}{ \delta u'(x_p)}- \frac{1}{2M} \sum_q^b \ \frac{ \delta k(x_p,t_q,u(t_q),u'(t_q))}{ \delta u'(x_r)} $
q=1,2,...,2M
و:
(20)
$ \frac{ \delta K(x_p,t_q,u(t_q),u'(t_q))}{ \delta u'(x_r)}=\begin{cases} \frac{ \delta k}{ \delta u}(x_p,t_q,u(t_q),u'(t_q)) \frac{ \delta u(x_p)}{ \delta u'(x_r)}+ \frac{ \delta k}{ \delta u'} (x_p,t_r,u(t_r),u'(t_r)) & q =r\\ \frac{ \delta k}{ \delta u}(x_p,t_q,u(t_q),u'(t_q)) & q \neq r\end{cases} 20$
میشه رابطه 20را تحلیل نمایید
