lec18_roots

# Of physics and astronomy log2 phys 503 dr gladden

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Unformatted text preview: or an initial window of Δx , the number of iterations (n) is: log( ∆x ) ￿ n= University of Mississippi Dept. of Physics and Astronomy log(2) Phys 503, Dr. Gladden ⇒ xhigh = xmid   Makes use of Taylor series expansion. f (xi+1 ) = f (xi ) + f ￿ (xi )(xi+1 − xi ) + O(dx2 )   If xi+1 is a root, then f (xi ) + f ￿ (xi )(xi+1 − xi ) ￿ 0 xi+1 f (xi ) = xi − ￿ f (xi )   So, the next value for x is: Now let   and repeat until   xi+1 → xi |xi+1 − xi | < ￿ Can evaluate derivative using a simple Euler step. University of Mississippi Dept. of Physics and Astronomy Phys 503, Dr. Gladden   Very efficient, but there are limitations   Happen to start at (or near) an extremum so derivative is close to 0.   Function is symmetric about root – leads to infinite loop!   Make sure to set an upper limit to number of iterations University of Mississippi Dept. of Physics and Astronomy Phys 503, Dr. Gladden University of Mississippi Dept. of Physics and Astronomy Phys 503, Dr. Gladden...
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## This note was uploaded on 10/05/2010 for the course PHYS phy503 taught by Professor Gladden during the Spring '09 term at Ole Miss.

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