Monotone cubic spline interpolation for functions with a strong gradient

Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or steep gradient data, some artifacts can appear Gibbs phenomenon. Also, preservation data monotonicity is requirement applications, that property not automatically verified by interpolator. In this paper, we study sufficient conditions obtain monotone cubic splines based on Hermite interpolators propose different ways construct them using non-linear formulas. The order approximation, each case, calculated numerical experiments are performed contrast theoretical results.