Preserving monotonic shape of the data using piecewise rational cubic functions

A C¹ monotonically shape preserving scheme has been developed. This scheme uses piecewise rational cubic functions. An algorithm has been developed, for economical curve implementation and pleasant demonstration, which ultimately replaces the rational cubic locally in each of the intervals by a constant, linear, rational quadratic or rational cubic function according to the nature of the slopes and parameters in that interval. A detailed description of the algorithm implementation has been made in tabular as well as pictorial form. Furthermore, an O(h⁴) convergence result is also obtained with appropriate derivative approximations.