Question

solue the equation xe + x ² + 1 = 0 using dixed point iteration method. Determine an interval [a, b] and an iteration jung junction, "g" such that there is a dixed uniky g Lthat.. Do 5 iterations using this method.

numerical methods question.
the equation is xe^(-x)+x^(3) +1=0

Answer 1

Tea +27 +1 - 0 Let f(x)x é + 2? + We will consider an interval [a, b] Auch that fla) f(b) = 0 1 o Intermediate mean value theorem says that F Am B be a continuous function q f(a) f(b) <0 then f has a root in {9.67) Take [a, b] = [o] Fla) = f(-) - LE + 1371 - - ēt -+ f(0) - £10) = 0+0+1 ... Fla).(6) = -ė (1) 20

floc) has a root in 1,07 Now, we will write fla) = 0 in the form of a = g(e) consider flue) = 0 genet 23 +1 = 0 > get = -d- => a = 67 (-1-43) => 04 (4+20) :: g(x) = -24 (172°) Fixed point iteration method is: Anti = g(en es)

..Mme = ceken (1t by Let Xo = - 12/25 € [-t, o : - - *(1 + $0) = -0.530714327 le = -24 (1+042) - - 0.500 262952 X -- ftp (1+ on, y) = -0.530455145 IA = -643 (1783) = -0.500521412 as 2-24 (1043) = -0.530200365 :: Tag = -0.5502003657