N25 - ME – 510 NUMERICAL METHODS FOR ME II EULER’S...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ME – 510 NUMERICAL METHODS FOR ME II EULER’S METHOD: y n+1 = y n + h f(t n ,y n ) h2 y''([ ) 2! Local Error: E local = Total or Overall Error: E total h2 =¦ y''([ n ) 2! h = ¦ y''([ n ) h 2! 1 vh h ¦ 2! y''([n ) (t n - t 0 ) Euler’s method is an order 1 method, i.e., the overall error is proportional to the first power of the step size, h 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II Geometrical Interpretation of Euler’s method 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II Accumulation of Error in Euler’s method 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II EXAMPLE ON EULER'S METHOD d y (t) dt - a y (t) , y (0) 1 y exact Euler's Method: e- a t y n + 1 = y n + h f (t n , y n) n t/a y exact y Euler 0 0 1 1 1 0.1 0.905 0.900 2 0.2 0.819 0.810 3 0.3 0.741 0.729 4 0.4 0.670 0.656 5 0.5 0.607 0.590 10 1.0 0.368 0.349 100 10.0 4.5 10 - 5 2.6 10 - 5 1000 100.0 3.7 10 - 44 1.0 10 - 46 3URI 'U )DUXN $UÕQo Fall 2007 ...
View Full Document

Page1 / 2

N25 - ME – 510 NUMERICAL METHODS FOR ME II EULER’S...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online