Two New Methods for Solving Systems of Nonlinear Equations


Abstract in English

In this paper, we present two new methods for finding the numerical solutions of systems of the nonlinear equations. The basic idea depend on founding relationship between minimum of a function and the solution of systems of the nonlinear equations. The first method seeks the numerical solution with a sequence of search directions, which is depended on gradient and Hessian matrix of function, while the second method is based on a sequence of conjugate search directions. The study shows that our two methods are convergent, and they can find exact solutions for quadratic functions, so they can find high accurate solutions for over quadratic functions. The purposed two algorithms are programmed by Mathematica Version9. The approximate solutions of some test problems are given. Comparisons of our results with other methods illustrate the efficiency and highly accurate of our suggested methods.

References used

AMAYA I., J. CRUZ, R. CORREA, Real Roots of Nonlinear Systems of Equations Through a Metaheuristic Algorithm, University Industrial de Santander, No. 170, 2011, pp. 15-23
ARDELEAN, G., The Attraction Basins Of Iterative Methods for Solving Nonlinear Equations, Ph.D. Thesis, Technical University of Cluj-Napoca,North University Center at Baia Mare, Faculty of Sciences, 2012, pp. 1-56
GROSAN C., A. Abraham, T. Norway, Multiple Solutions for a System of Nonlinear Equations, International Journal of Innovative, Computing, Information and Control, Vol. x, No. x, 2008, pp. 1-12

Download