Iterative methods for solving nonlinear equations with multiple zeros

This thesis discusses the problem of finding the multiple zeros of nonlinear equations. Six two-step methods without memory are developed. Five of them posses third order convergence and an optimal fourth order of convergence. The optimal order of convergence is determined by applying the Kung-Traub conjecture. These method were constructed by modifying the Victory and Neta’s method, Osada’s method, Halley’s method and Chebyshev’s method. All these methods are free from second derivative function. Numerical computation shows that the newly modified methods performed better in term of error. The multiplicity of roots for the test functions have been known beforehand. Basin of attraction described that our methods have bigger choice of initial guess.

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