Stability domains of explicit multistep methods

A new algorithm is proposed for obtaining stability domains of multistep numerical schemes. The algorithm is based on Bernoulli’s algorithm for computing the greatest in magnitude root of a polynomial with complex coefficients and the Dandelin–Lobachevsky–Graeffe method for squaring the roots. Numerical results on the construction of stability domains of Adams–Bashforth methods of order 3–11 are given.