University of Florida/Egm6321/f09.team1.gzc/Mtg10

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Mtg 10: Sat, 22 Jan 11

page10-1

HW2.9:Use (1) p.8-1 to generate P5(x),

and matlabl command"roots"to comp.

the roots of P5(x)to check values in table

on  p. 7-5. Plot the roots on [-1,+1] using

matlab "plot" command (plot dots "."

with coordinator (xi,yi), i = 1,...,5 : use "markersinge" 15)

xi: roots of P5(x)

yi:

Plot  (x, y, '.' , 'markersige' , 15)

Repeat the above for P10(x)

observe the location of the roots near end points -1 and +1

(prepare for Runge phenomenon)

NOTE:

Lagrange interp. cont'd p.9-4

 

page10-2

Simpson's rule (simple)

c0,  c1,  c2   unknowns

p2=(xi) = f(xi)    i= 0, 1, 2               (3)

3 equations for 3 unknowns {ci}

Method 2:Use lagrangeinterp.(2) p.8-3   (1) p.9-2

 

Equiv. of meth1 and meth 2:            (3)

 


page10-3

It can be verified that

l0(x0)=1 , l0(x1) = l0(x2) = 0

li(xj) = δij                  i,j = 0. 1. 2

Nm1.s11.Mtg10.pg3.fig1.svg


page10-4

Nm1.s11.Mtg10.pg4.fig2.svg

HW*2.10: Use(2) & (3)p.10-2 to find

expression for {ci} in terms (xi, f(xi)) i=0,1,2.

HW*2.11: Use (4) p.10-2 to

derive simple Simpson's rule

HW*2.11:f(x)-ex1/x on [o,1] S10and on [-1,1]S11

Consider n=1(Trap), 2(Simp), 4, 8, 16

 

page10-5

Constrast fn(x) as in (2) p.8-3.

Plot f , fn , n= 1, 2, 4, 8, 16

Compare

n=1, 2, 4, 8

and compare to I (use WA with more digits)

For n=5 plot l0, l1, l2 How would l3, l4, l5  look like?

HW*2.13:show