This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MPO 662 – Problem Set 2 Feel free to use symbolic computation software such as mathematica or the symbolic toolbox in matlab to carry out the algebra. See 1 to see an example with matlab. 1. Use Taylor series to derive explicit finite difference approximations according to the following specifications: • A 3 rd order approximation to the first derivatives using the points i 2 ,i 1 ,i and i + 1. • Use the same points as above and derive the highest possible approximation to the third derivative. • Derive a 4 th order centered approximations to the second derivative, using points i , i ± 1, and i ± 2. 2. Compact differencing for second derivatives using the formula α u xx  i 1 + u xx  i + α u xx  i +1 = a 1 u i +1 2 u i + u i 1 Δ x 2 + a 2 u i +2 2 u i + u i 2 4Δ x 2 (1) • Determine the equations that would make the scheme fourthorder. write the solu tion in terms of the parameter α ....
View
Full
Document
This note was uploaded on 01/08/2012 for the course MPO 662 taught by Professor Iskandarani,m during the Spring '08 term at University of Miami.
 Spring '08
 Iskandarani,M

Click to edit the document details