Considering the condition number of the coefficient matrices, the different weighted residual methods do not show the same sensitivity to the roots of the polynomials in the Jacobi family. On the other hand, the simulated error obtained adopting the Galerkin, tau and orthogonal collocation methods for different 伪, 尾-combinations differ insignificantly. The condition number of the LSQ coefficient matrix is relatively large compared to the other numerical methods, hence preventing the simulation error to approach the machine accuracy.

The Legendre polynomial, i.e., 伪 = 尾 = 0, is a very robust Jacobi polynomial giving on average the lowest condition number of the coefficient matrices and the polynomial also give among the best behaviors of the error as a function of polynomial order. This polynomial gives good results for small and large gradients within both slab and spherical pellet geometries.

Adopting the Legendre polynomial, the Galerkin and tau methods obtain favorable lower condition numbers than the orthogonal collocation and LSQ methods.