Abstract: In this paper, an approach is introduced to determine the stable interval of the constant term of a characteristic equation by using the theory of extended graphical representation of polynomials. Because the constant a_n itself is not taken into account and because this method is to get a stable interval of a_n, not merely to make a stability test for a set of known coefficients, this method of stability criteria has some advantages over the others. The interval of a_n can be obtained from the calculation of some algebraical expressions when n≤10 where n is the degree of the characteristic equation. It is very convenient to calculate for the cases n=5 and n=6. When n≥11, this interval can be found only by the method of numerical solutions.

Key words: splitting modulus variational principle, method of splitting modulus finite elements, anisotropic, ill-conditioned problems