Splines interpolation analysis using Maple package

Abstract

.Expressing relationships in data with functions is both useful and convenient. It allows us to estimate dependent variables at values of independent variables not given in the data, take derivatives, integrate, and even solve differential equations. This is done by interpolation in a precise way. Interpolation is a set of function points that passes through each data point. Linear polynomial interpolation, cubic spline, Lagrange and Newton are common interpolation methods. In interpolation problems, spline interpolation is often preferred over polynomial interpolation because it gives similar results even when using low-order polynomials, while avoiding the phenomenon common at higher orders. will be We used simple linear functions to introduce some basic concepts and issues related to spline interpolation. Then we derive an algorithm for fitting quadratic lines to the data. Finally, we present material on the cubic spline, which is the most common and useful version in engineering practice. Cubic spline is easy to display and calculate by Maple package. Because Maple is closed, the same math symbols used in classrooms can be used to enter data. In addition, the Maple package has many features, including converting outputs to MATLAB codes and LaTeX commands, where computational problems related to the subject are presented with precise and explicit answers.