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# rombergs - SE301:NumericalMethods 19.RombergMethod...

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SE301_Topic 6 Al-Amer2005 1 SE301:Numerical Methods 19. Romberg Method Motivation Derivation of Romberg Method Romberg Method Example When to stop?

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SE301_Topic 6 Al-Amer2005 2 Motivation for Romberg Method Motivation for Romberg Method Trapezoid formula with an interval  h  gives error of the  order  O(h 2 ) We can combine two Trapezoid estimates with intervals   2h and h  to get a better estimate.
SE301_Topic 6 Al-Amer2005 3 Romberg Method Romberg Method First column is obtained using Trapezoid Method dx f(x) of ion approximat the improve to combined are 4h,8h,... 2h, h, size of intervals with method Trapezoid using Estimates b a R(0,0) R(1,0) R(1,1) R(2,0) R(2,1) R(2,2) R(3,0) R(3,1) R(3,2) R(3,3) The other elements are obtained using the Romberg Method

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SE301_Topic 6 Al-Amer2005 4 First Column   First Column   Recursive Trapezoid Method Recursive Trapezoid Method [ ] ( 29 n k a b h h k a f h n R n R b f a f a b n 2 ) 1 2 ( ) 0 , 1 ( 2 1 ) 0 , ( ) ( ) ( 2 ) 0 , 0 ( R ) 1 ( 2 1 - = - + + - = + - = - =
SE301_Topic 6

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rombergs - SE301:NumericalMethods 19.RombergMethod...

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