An efficient one step Adam type implicit block numerical algorithm developed by simultaneous
employment of interpolation and collocation techniques is proposed in this paper. Non mesh points were introduced
to upgrade the order of consistency and improve the rate of convergence of the method. Further analysis revealed a
wide interval of absolute stability. The method is implemented as a block to improve efficiency and reduce computational
cost. Comparison of the new method with previous methods in terms of absolute errors of approximation established
an improvement over those methods
