Lecture 13 - Example: First Derivatives Use forward and...

Info iconThis preview shows pages 1–4. 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

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: Example: First Derivatives Use forward and backward difference approximations to estimate the first derivative of at x = 0.5 with h = 0.5 and 0.25 (exact sol. = f = -0.9125) Forward Difference Backward Difference 2 . 1 x 25 . x 5 . x 15 . x 1 . ) x ( f 2 3 4 +---- = =- =- =-- = = =- =- =-- = = % . , . . . . . . ) . ( ) . ( ) . ( , . % . , . . . . . ) . ( ) ( ) . ( , . 5 26 155 1 25 925 63632813 5 75 5 f 75 f 5 f 25 h 9 58 45 1 5 925 2 5 1 5 f 1 f 5 f 5 h t t =- =- =-- = = =- =- =-- = = % . , . . . . . . ) . ( ) . ( ) . ( , . % . , . . . . . ) ( ) . ( ) . ( , . 7 21 714 25 10351563 1 925 25 5 25 f 5 f 5 f 25 h 7 39 55 5 2 1 925 5 f 5 f 5 f 5 h t t Example: First Derivative Use central difference approximation to estimate the first derivative of at x = 0.5 with h = 0.5 and 0.25 (exact sol. = f = -0.9125) Central Difference 2 . 1 x 25 . x 5 . x 15 . x 1 . ) x ( f 2 3 4 +---- = % 4 . 2 , 934 . 5 . 10351563 . 1 63632813 . 25 . 75 . ) 25 . ( f ) 75 . ( f ) 5 . ( f , 25 . h % 6 . 9 , . 1 1 2 . 1 2 . 1 ) ( f ) 1 ( f ) 5 . ( f , 5 . h =- =- =-- = = =- =- =-- = = t t Second-Derivatives Taylor-series expansion Uniform grid spacing Second-order accurate O(h 2 )...
View Full Document

This note was uploaded on 11/15/2010 for the course EGM 5403 taught by Professor Mei during the Spring '10 term at University of Florida.

Page1 / 19

Lecture 13 - Example: First Derivatives Use forward and...

This preview shows document pages 1 - 4. Sign up to view the full document.

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