Description: This simulation depicts shows you why conducting higher-order interpolation is a bad idea. It simulates Runge’s phenomena where he chose several points on a simple smooth function y=1/(1+25x2) in the [-1,1] domain to conduct polynomial interpolation. We take it a step further to show the use of Chebyshev points and also what happens when a cubic spline is used.
Keywords: Runge’s phenomena, interpolation, higher-order interpolation, cubic spline, Chebyshev points
Learning Objectives: After successful completion of running the simulation with proper questions asked by the instructor, the student would be able to 1) note the effect of the order of polynomial on the error between the original function and the interpolated polynomial 2) note the effect of the use of Chebyshev points on the higher-order interpolation 3) note how the use of cubic splines improves the representation of the chosen function.
Full Resources: The full resources for the topic of the higher-order interpolation being a bad idea, polynomial interpolation, and spline interpolation include textbook content, PowerPoint presentations, multiple-choice tests, audiovisual lectures, and application examples.
Software Requirements: Latest versions of Safari, Microsoft Edge, Firefox, Google Chrome.
Credits: Design Team: Autar Kaw and Mayank Pandey. Software development: Mayank Pandey and Autar Kaw.
We acknowledge the immense help of the Phet Google group, third party libraries: almond-0.2.9.js, easing-equations-r12,FileSaver-b8054a2.js, fontawesome-webfont-3.0.2.svg, jama-1.0.2, jquery-2.1.0.js, lodash-2.4.1.js, pegjs-0.7.0.js, seedrandom-2.4.2.js, text-2.0.12.js, Tween-r12.js
Acknowledgments: This material is based upon work supported partially by the National Science Foundation under Grant Number 2013271. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
All Simulations: Here is the link for all the simulations developed.