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ABSTRACT
The Classical Simpson third order method is one of the known methods for approximating roots of some nonlinear equations, as a result of its simplicity with convergence order of three. However, the classical Simpson fails when dealing with some nonlinear equations whose first derivative function value is zero or near zero at iteration point. This study is geared towards the development of method that overcomes singularity at iteration points. New method is proposed by modifying Classical Simpson third order Method using the forward difference method, while its convergence analysis is carried out via the use of Taylor’s expansion The proposed method is of order p=2 and approximates nonlinear equation whose first derivative function value is zero or near zero at iteration point.
