Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AN IMPROVED EXPONENTIAL REGULA FALSI METHODS WITH CUBIC CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

  • Ibrahim, S.A. Hoda (Department of Mathematics, Faculty of science, Zagazig University)
  • Received : 2010.03.23
  • Accepted : 2010.05.14
  • Published : 2010.09.30
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Abstract

The aim of this paper is to propose a cubic convergent regula falsi iterative method for solving the nonlinear equation f(x) = 0, where f : [a,b] $\subset$ R $\rightarrow$ R is a continuously differentiable. In [3,6] a quadratically convergent regula falsi iterative methods for solving this nonlinear equations is proposed. It is shown there that both the sequences of diameters and iterative points sequence converge to zero simultaneously. So The aim of this paper is to accelerate further the convergence of these methods from quadratic to cubic. This is done by replacing the parameter p in the iteration of [3,5,6] by a function p(x) defined suitably. The convergence analysis is carried out for the method. The method is tested on number of numerical examples and results obtained shows that our methods are better and more effective and comparable to well-known methods.

Keywords

References

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