In view of the fact that block methods are adequate to numerically approximate second order ordinary differential equations, which can be developed with or without the presence of higher derivatives, although still possessing the same order, we introduce block methods of equal order with and without the presence of higher derivatives using the linear block approach. The resulting block methods are employed to solve the second order ordinary differential equations.The accuracy of the block methods is investigated with respect to their absolute error. It is found that the block method with the presence of higher derivative has better accuracy.

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The conventional two-step implicit Obrechkoff method is a discrete scheme that requires additional starting values when implemented for the numerical solution of first order initial value problems. This paper therefore presents a two-step implicit Obrechkoff-type block method which is self-starting for solving first order initial value problems, hence bypassing the rigour of developing and implementing new starting values for the method. Numerical examples are considered to show the new method performing better when compared with previously existing methods in literature.

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