Modified Chebyshev’s method free from second derivative for non-linear equations

In this paper, we present some new modifications of Chebyshev’s method free from second derivative. The order of convergence of the new methods is three. Per iteration the methods require two evaluations of the function and one evaluation of its first derivative. The convergence of the new methods for the case of multiple roots is also discussed. Numerical examples show that the new methods have definite practical utility.