A Novel Perturbed Dynamical Method for Solving Singular Systems of Nonlinear Equations

Abstract

Summary ABSTRACT: In this paper, a novel method, named the perturbed dynamical method, is proposed to solve nonlinear systems whose Jacobian matrix is singular. The con- cept of the proposed method roots from the conventional homotopy method but it takes the advantages of converting a vector function to a scalar function by using the square norm of the vector function to conduct a scalar-based homotopy method. Then, a small parameter, which is similar to the perturbation theory, is introduced to the singular systems of nonlinear equations such that the modified singular sys- tems of nonlinear equations become nonsingular and the asymptotic solutions may be found. As a result, the proposed novel method does not need to calculate the inverse of the Jacobian matrix and thus has great numerical stability. Results ob- tained show that the proposed novel method can be used to solve singular systems of nonlinear equations with high accuracy as well as the convergence and it may be a better alternative for solving a system of non-linear algebraic equations.