**ABSTRACT**

A four-step predictor-corrector method with a higher derivative is presented for the direct solution of second-order initial value problems (IVPs). In deriving the algorithm, power series and Bernstein polynomial in combine was used as an approximate function. The approximate solution is interpolated while its second and third derivatives are collocated at the given interval. The main predictor was developed using the same approach and is of the equal order as the corrector. The developed method (Corrector) was found to be consistent, zero stable, and convergence. Numerical examples are tested to demostrate the accuracy of the method.

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