1 / 16

Direct Method of Interpolation

Direct Method of Interpolation. Major: All Engineering Majors Authors: Autar Kaw, Jai Paul http://numericalmethods.eng.usf.edu Numerical Methods for STEM undergraduates. What is Interpolation ?.

arousey
Download Presentation

Direct Method of Interpolation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Direct Method of Interpolation Major: All Engineering Majors Authors: Autar Kaw, Jai Paul http://numericalmethods.eng.usf.edu Numerical Methods for STEM undergraduates http://numericalmethods.eng.usf.edu

  2. What is Interpolation ? Given (x0,y0), (x1,y1), …… (xn,yn), find the value of ‘y’ at a value of ‘x’ that is not given. http://numericalmethods.eng.usf.edu

  3. Velocity vs Time http://numericalmethods.eng.usf.edu

  4. Interpolants Polynomials are the most common choice of interpolants because they are easy to: Evaluate Differentiate, and Integrate http://numericalmethods.eng.usf.edu

  5. Direct Method Given ‘n+1’ data points (x0,y0), (x1,y1),………….. (xn,yn), pass a polynomial of order ‘n’ through the data as given below: where a0, a1,………………. an are real constants. • Set up ‘n+1’ equations to find ‘n+1’ constants. • To find the value ‘y’ at a given value of ‘x’, simply substitute the value of ‘x’ in the above polynomial. http://numericalmethods.eng.usf.edu

  6. Example The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the direct method for linear interpolation. Velocity vs. time data for the rocket example Velocity as a function of time http://numericalmethods.eng.usf.edu

  7. Linear Interpolation Solving the above two equations gives, Hence http://numericalmethods.eng.usf.edu

  8. Example The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the direct method for quadratic interpolation. Velocity vs. time data for the rocket example Velocity as a function of time http://numericalmethods.eng.usf.edu

  9. Quadratic Interpolation Quadratic Interpolation Solving the above three equations gives http://numericalmethods.eng.usf.edu

  10. Quadratic Interpolation (contd) http://numericalmethods.eng.usf.edu

  11. Example The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the direct method for cubic interpolation. Velocity vs. time data for the rocket example Velocity as a function of time http://numericalmethods.eng.usf.edu

  12. Cubic Interpolation http://numericalmethods.eng.usf.edu

  13. Cubic Interpolation (contd) http://numericalmethods.eng.usf.edu

  14. Comparison Table http://numericalmethods.eng.usf.edu

  15. Distance from Velocity Profile Find the distance covered by the rocket from t=11s to t=16s ? = http://numericalmethods.eng.usf.edu

  16. Acceleration from Velocity Profile Find the acceleration of the rocket at t=16s given that , http://numericalmethods.eng.usf.edu

More Related