ENO-modification of a non-local cubic spline on a uniform mesh (Q2746936)

The problem of constructing a nonlocal cubic spline preserving the monotonicity of data on a uniform mesh is discussed. For a classical cubic spline, the continuity conditions of the second derivative of an interpolating spline produce a system of linear equations with respect to nodal spline slopes. The author supposes that unwanted oscillations are suppressed if the large central-difference approximation of the first derivative on the right-hand side of the equations is replaced by the smaller approximation. The varying of an equation is equivalent to a discontinuity of the second derivative in the corresponding knot. NEWLINENEWLINENEWLINEIf the values of the neighboring divided differences of data are substantially different, a modification of some equations is proposed. For monotone data, monotonicity of the modified spline is established. However, in our opinion, the new spline is not interesting because, generally speaking, the spline slopes do not approximate the first derivative.