In [3] a method which gives the solution to problem (1), (2) in the form of a spline function has been described. In [6] the fitting factor of the form $\sigma_i=(h_ip_i/2)cth(h_ip_i/2)$ has been introduced by which the conditions from [3] are relaxed. In that way a numerically more stable scheme has been obtained. Here is presented a better error estimation for the case $q\neq 0$ without the barrier function. Also, the convergence order for Dirichlet’s boundary conditions is increased.