Two Fourth-order Iterative Methods Based on Continued Fraction for Root-finding Problems
نویسندگان
چکیده
In this paper, we present two new one-step iterative methods based on Thiele’s continued fraction for solving nonlinear equations. By applying the truncated Thiele’s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed. Keywords—Iterative method, Fixed-point iteration, Thiele’s continued fraction, Order of convergence.
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