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K. M. Brown, “Computer Oriented Algorithms for Solving Systems of Simultaneous Nonlinear Algebraic Equations,” In: G. D. Byrne and C. A. Hall, Eds., Numerical Solution of Systems of Nonlinear Algebraic Equations, Academic Press, New York, 1973, pp. 281-348.

has been cited by the following article:

• TITLE: Solving Large Scale Nonlinear Equations by a New ODE Numerical Integration Method

  AUTHORS: Tianmin Han, Yuhuan Han

  KEYWORDS: Nonlinear Equations, Ordinary Differential Equations, Numerical Integration, Fixed Point Iteration, Newton’s Method, Stiff, Ill-Conditioned

  JOURNAL NAME: Applied Mathematics, Vol.1 No.3, September 29, 2010

  ABSTRACT: In this paper a new ODE numerical integration method was successfully applied to solving nonlinear equations. The method is of same simplicity as fixed point iteration, but the efficiency has been significantly improved, so it is especially suitable for large scale systems. For Brown’s equations, an existing article reported that when the dimension of the equation N = 40, the subroutines they used could not give a solution, as compared with our method, we can easily solve this equation even when N = 100. Other two large equations have the dimension of N = 1000, all the existing available methods have great difficulties to handle them, however, our method proposed in this paper can deal with those tough equations without any difficulties. The sigularity and choosing initial values problems were also mentioned in this paper.