N9 - ME – 510 NUMERICAL METHODS FOR ME II Prof. Dr. Faruk...

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Unformatted text preview: ME – 510 NUMERICAL METHODS FOR ME II Prof. Dr. Faruk Arınç Fall 2010 INTERPOLATION SCHEMES Name Advantages Disadvantages Newton-Gregory The order of the polynomial can be changed easily. Evaluation of errors is easy. A difference or a divided difference table must be prepared. Lagrange Convenient form. Easy to program. Cumbersome for hand calculations. Spline Applicable to any number of data points. Needs to solve a set of simultaneous equations. Hermite Accuracy is high because polynomial is fitted to derivatives also. Needs values of derivatives. Chebyshev Errors are more evenly distributed than that with an equispaced grid. Unevenly distributed grid points. ME – 510 NUMERICAL METHODS FOR ME II Prof. Dr. Faruk Arınç Fall 2010 Define Newton-Gregory Forward Polynomial x - x s where h is constant (equally spaced data points) h g32 f ! n 1) n- (s ... 1)- (s s ... f ! 2 1)- (s s f s f (x) P n 2 n g39 g14 g14 g14 g39 g14 g39 g14 g32 ) ( f )! 1 (n ) x- (x ... ) x- (x ) x- (x (x) E )...
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This note was uploaded on 02/28/2011 for the course ME 510 taught by Professor Dr.faruckarinc during the Spring '11 term at Middle East Technical University.

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N9 - ME – 510 NUMERICAL METHODS FOR ME II Prof. Dr. Faruk...

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