145_pdfsam_math 54 differential equation solutions odd

# 145_pdfsam_math 54 differential equation solutions odd -...

This preview shows page 1. Sign up to view the full content.

Exercises 3.6 In order to approximate the solution φ ( x )= e x at the point x =1w i th N steps, we take h =( x x 0 ) /N =1 /N ,andso N =1 /h . Then the above formula becomes y N = ± 1+ h/ 2 1 h/ 2 ² N y 0 = ± 1+ h/ 2 1 h/ 2 ² N = ± 1+ h/ 2 1 h/ 2 ² 1 /h and hence e = φ (1) y N = ± 1+ h/ 2 1 h/ 2 ² 1 /h . Substituting h =10 k , k =0 , 1 , 2 , 3, and 4, we Fll in Table 3-A. Table 3–A : Approximations ± 1+ h/ 2 1+ h/ 2 ² 1 /h to e 2 . 718281828 ... . h Approximation Error 1 3 0.281718172 10 1 2.720551414 0.002269586 10 2 2.718304481 0.000022653 10 3 2.718282055 0.000000227 10 4 2.718281831 0.000000003 These approximations are better then those in Tables 3.4 and 3.5 of the text.
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.

Ask a homework question - tutors are online