Mupad Models for Splines

Abstract

The aim of this paper is to reconstruct relevant & well elaborated models for Splines as well as their interpolation via Mupad Numeric & Graphic Functions , these models have to include linear piecewise model, quadratic piecewise model, cubic piecewise model, certain models for Runge's phenomenon will find their places in between, these models aiming to represent computerized resolution for Runge's phenomenon. Also it will refer to advantages & disadvantage of interpolation methods as Lagrange polynomials, Neville's, Divided differences and Cubic spline, giving more attention to the last one  in accordance to its significance place among other methods. Here is direct verification for Weierstrass theorem, also the author will come across the specific theoretical approaches to verify his results as well as the reconstructed models.

Keywords: Rainbow spline, linear, quadratic, cubic, natural, clamped splines, Newton, Neville, Lagrange interpolations, Chebyshev knots, Runge's phenomenon, Weierstrass theorem.