N26 - ME – 510 NUMERICAL METHODS FOR ME II EXAMPLE ON...

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Unformatted text preview: ME – 510 NUMERICAL METHODS FOR ME II EXAMPLE ON MODIFICATIONS OF EULER'S METHOD h y  yn 1 · § yn  h f ¨ t n  , n ¸ 2 2 ¹ © yn 1 d y (t) dt - a y (t) , y (0) 1 y exact e- a t Euler's Method: Mod. 1 Mod. 2 3URI 'U )DUXN $UÕQo y n + 1 = y n + h f (t n , y n) y n + 1 = y n + h f (t n + 1 , y n + 1) yn 1 h y  yn 1 · § yn  h f ¨ t n  , n ¸ 2 2 ¹ © Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II EXAMPLE ON MODIFICATIONS OF EULER'S METHOD n t/a y exact y Euler y end y middle 0 0 1 1 1 1 1 0.1 0.905 0.900 0.909 0.905 2 0.2 0.819 0.810 0.826 0.819 3 0.3 0.741 0.729 0.751 0.741 4 0.4 0.670 0.656 0.683 0.670 5 0.5 0.607 0.590 0.621 0.606 10 1.0 0.368 0.349 0.386 0.368 100 10.0 4.5 10 - 5 2.6 10 - 5 7.3 10 - 5 4.6 10 - 5 1000 100.0 3.7 10 - 44 1.0 10 - 46 4.1 10 - 42 3.4 10 - 44 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II Geometrical Interpretation of Heun’s method 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II Accumulation of Error in Euler’s method Geometrical Interpretation of the Modified Euler’s method 3URI 'U )DUXN $UÕQo Fall 2007 ...
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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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N26 - ME – 510 NUMERICAL METHODS FOR ME II EXAMPLE ON...

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