In this paper, we developed a new continuous block method by the method of interpolation and\ncollocation to derive new scheme. We adopted the use of power series as a basis function for approximate\nsolution. We evaluated at off grid points to get a continuous hybrid multistep method.\nThe continuous hybrid multistep method is solved for the independent solution to yield a continuous\nblock method which is evaluated at selected points to yield a discrete block method. The\nbasic properties of the block method were investigated and found to be consistent, zero stable and\nconvergent. The results were found to compete favorably with the existing methods in terms of\naccuracy and error bound. In particular, the scheme was found to have a large region of absolute\nstability. The new method was tested on real life problem namely: Dynamic model.
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