1. Computer Programming (TKK-2144) 13/14 Semester 1 Instructor: Rama Oktavian Email: rama.oktavian@ub.ac.id Office Hr.: M.13-15, W. 13-15 Th. 13-15, F. 13-15

2. Outlines 1. Quadratic Interpolation 2. Cubic Interpolation 3. Spline Interpolation 4. Example in chem.eng

3. Quadratic interpolation We want to find a polynomial which satisfies for for given data points (x0,y0),(x1,y1),(x2,y2).

4. Quadratic interpolation http://numericalmethods.eng.usf.edu 4 The upward velocity of a rocket is given as a function of time in Table 2. Find the velocity at t=16 seconds using the direct method for quadratic interpolation. 00 10227.04 15362.78 20517.35 22.5602.97 30901.67 Table 1 Velocity as a function of time. Figure 1Velocity vs. time data for the rocket example

5. Quadratic interpolation Solving the above three equations gives Figure 2 Quadratic interpolation. http://numericalmethods.eng.usf.edu

6. Quadratic interpolation Figure 2 Quadratic interpolation. http://numericalmethods.eng.usf.edu

7. Cubic Interpolation Figure 3 Cubic interpolation. http://numericalmethods.eng.usf.edu

8. Cubic Interpolation Figure 3 Cubic interpolation. http://numericalmethods.eng.usf.edu

9. Spline Interpolation  Spline:  In Mathematics, a spline is a special function defined piecewise by polynomials;  In Computer Science, the term spline more frequently refers to a piecewise polynomial (parametric) curve.  Simple construction, ease and accuracy of evaluation, capacity to approximate complex shapes through curve fitting and interactive curve design.

10. Spline Interpolation  Spline Interpolation:  Linear spline  Quadratic spline  Cubic spline

11. Spline Interpolation  Linear Spline Interpolation:

12. Spline Interpolation  Linear Spline Interpolation: http://numericalmethods.eng.usf.edu

13. Spline Interpolation  Quadratic Spline Interpolation: http://numericalmethods.eng.usf.edu

14. Spline Interpolation  Quadratic Spline Interpolation: http://numericalmethods.eng.usf.edu

15. Spline Interpolation  Quadratic Spline Interpolation: http://numericalmethods.eng.usf.edu