Solving Large Scale Nonlinear Equations by a New ODE Numerical Integration Method - Applied Mathematics

AM > Vol.1 No.3, September 2010

Applied Mathematics

Volume 1, Issue 3 (September 2010)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

Solving Large Scale Nonlinear Equations by a New ODE Numerical Integration Method ()

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DOI: 10.4236/am.2010.13027 8,997 Downloads 17,931 Views Citations

Author(s)

Tianmin Han, Yuhuan Han

Affiliation(s)

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.

KEYWORDS

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

Share and Cite:

T. Han and Y. Han, "Solving Large Scale Nonlinear Equations by a New ODE Numerical Integration Method," Applied Mathematics, Vol. 1 No. 3, 2010, pp. 222-229. doi: 10.4236/am.2010.13027.

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