Lecture+13--numerical+differentiation

Lecture+13--numerical+differentiation - Truncation Errors l...

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Truncation Errors Uniform grid spacing (Taylor Series) (1) (2) xi-2 xi-1 xi xi+1 xi+2 2 3 1 (2) ( ) ( ) ( ) ( ) ( ) 2! 3! i i i i i h h f x f x hf x f x f x + ′′ ′′′ = + + + + L h x = 2 3 1 (1) ( ) ( ) ( ) ( ) ( ) 2! 3! i i i i i h h f x f x hf x f x f x - ′′ ′′′ = - + - + L 1 1 ( ) ( ) : ( ) ( ) O(h) 2 i i i f x f x h forward f x f h ξ + - ′′ = - 1 2 ( ) ( ) : ( ) ( ) O(h) 2 i i i f x f x h backward f x f h - - ′′ = +

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Truncation Errors (2)- (1) xi-1 xi xi+1 2 3 1 (2) ( ) ( ) ( ) ( ) ( ) 2! 3! i i i i i h h f x f x hf x f x f x + ′′ ′′′ = + + + + L 2 3 1 (1) ( ) ( ) ( ) ( ) ( ) 2! 3! i i i i i h h f x f x hf x f x f x - ′′ ′′′ = - + - + L 1 1 ( ) ( ) ... i i f x f x + - - = 2 2 1 1 3 ( ) ( ) : ( ) ( ) O(h ) 2 6 i i i f x f x h central f x f h ξ + - - ′′′ = -
Truncation Errors 1 1 1 2 1 1 3 2 2 ( ) ( ) : ( ) ( ) ( ) 2 ( ) ( ) : ( ) ( ) ( ) 2 ( ) ( ) : ( ) ( ) ( ) 2 6 i i i i i i i i i f x f x forward f x f O h f x f x backward f x f O h f x f x

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This note was uploaded on 11/07/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Spring '09 term at University of Florida.

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Lecture+13--numerical+differentiation - Truncation Errors l...

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