On construction of a new interpolation tool: cubic $q$-spline

Abstract

This work presents a new interpolation tool, namely, cubic $q$-spline. Our new analogue generalizes a well known classical cubic spline. This analogue, based on the Jackson $q$-derivative, replaces an interpolating piecewise cubic polynomial function by $q$-polynomials of degree three at most. The parameter $q$ provides a solution flexibility.