TITLE:
Multistep Quadrature Based Methods for Nonlinear System of Equations with Singular Jacobian
AUTHORS:
Oghovese Ogbereyivwe, Kingsley Obiajulu Muka
KEYWORDS:
Nonlinear System of Equations, Quadrature Formula, Singular Jacobian, Mul-tistep Iterative Methods
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.3,
March
28,
2019
ABSTRACT: Methods for the approximation of solution of
nonlinear system of equations often fail when the Jacobians of the systems are singular at iteration
points. In this paper, multi-step families of quadrature based iterative
methods for approximating the solution of nonlinear system of equations with
singular Jacobian are developed using
decomposition technique. The methods proposed in this study are of convergence
order , and require only the evaluation of first-order Frechet
derivative per iteration. The approximate solutions generated by the proposed
iterative methods in this paper compared with some existing contemporary
methods in literature, show that methods developed herein are efficient and
adequate in approximating the solution of nonlinear system of equations whose
Jacobians are singular and non-singular at iteration points.