On the Development of A New Multi-Step Derivative Free Method to Accelerate the Convergence of Bracketing Methods for Solving F(x) = 0

E. SOOMRO, A. A. SHAIKH, S. QURESHI

Abstract


Finding root of non-linear equation F (x) = 0 is a classical problem in numerical analysis which arise in many scientific and engineering fields. In this paper the main focus is given to develop an Algorithm which speed up the convergence of bracketing methods for finding root of a non-linear equation. For this purpose, combination of newton’s method and truncated Taylor’s series is employed. The new method is derivative free, require three preliminary approximations to start and does not have any pitfall. Some numerical examples are also presented in this paper in order to analyze the efficiency of the developed method with other methods. It is observed from the results and comparison of new method with the famous bracketing methods including Bisection method and Regula-Falsi method that the new developed method is performing better than these two methods.

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