Solving systems of non-linear equations using the Lyapunov direct method

Abstract This paper describes how the well-known Lyapunov theory can be used for thedevelopment of a number of new algorithms for solving a system of non-linear equations. The algorithms are of the “steepest descent” type. The advantage of the methodology presented is that it improves the convergence of the solution and moreover, allows an exact prespecification of the finite time in which the solution is obtained. This is achieved with various Lyapunov functions.