ALGORITHMS FOR CLASSICAL STABILITY PROBLEMS

Differential equation is stable if roots of characteristic polynomial are in interior of left half-plane; likewise difference equation is stable if roots of characteristic polynomial are in interior of unit circle; paper concerns algorithms which test polynomials for these properties; also of concern is relationship between two problems; special numerical integration formulas are developed which transform differential equation into difference equation; formulas are such that differential equation and corresponding difference equation are both stable or else they are both unstable.