Abstract
The aim of this paper is to describe two variants of a parameter-based continuation method connecting two third order iterative methods namely, the Chebyshev's method and the Super-Halley's method, for solving non-linear equations in R without using the second derivative. The convergence analysis is carried out to show the third order convergence of the methods. A number of numerical examples are worked out to illustrate the efficiency and performance of the methods. On comparison of the number of iterations taken by our methods with those obtained by Newton's method, the Chebyshev's method and the Super-Halley's method, it is observed that our methods take less number of iterations. It is further observed that for two different values of the parameter, our methods reduce to the Chebyshev's method and the Super-Halley's method free from second derivative.
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