Grammar..

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"Furthermore, the proposed method is derived in order to solve first and higher order BVPs in a single code using variable step-size and implemented in the predictor corrector mode. The method is order six for predictor and order seven for corrector. This H method will act as simultaneous numerical integrator such compute the numerical solution at five points simultaneously. Numerical results obtained show that direct integration method is outperform compared to the reduce method. The results obtained show that the method manage to produce good results for solving first and higher order BVPs."