EE518 Homework 8 Zhe Zheng Q2 function dx dy n x BisectionMethod a b tol consec tol approx n 0 y1 FunDiff a y2 FunDiff b x a b 2 mid FunDiff x p y1 y2 dx abs b a dy abs mid if p 0 if y1 0 x a elseif y2 0 x b end elseif p 0 disp Change Interval return elseif p 0 while dx tol consec dy tol approx if mid 0 return end if sign mid sign y1 a x end if sign mid sign y2 b x end x a b 2 mid FunDiff x dx abs b a dy abs mid y1 FunDiff a y2 FunDiff b n n 1 end end end function y FunDiff m y exp m 2 m end dx dy n x BisectionMethod 2 2 10 6 10 6 dx 9 5367e 07 dy 5 5883e 07 n 22 x 0 6529 Answer The point of intersection of f x and g x on the interval 2 2 is x 0 6529 Q3 function dx dy n y NewtonMethod x tol consec tol approx n 0 j x if abs j 2 disp Out of Interval return end v FunDiff j if v 0 y j return else k DeFunDiff j if abs k 2 disp Out of Interval return end dx abs k j dy abs FunDiff k while dx tol consec dy tol approx u FunDiff k if u 0 y k return end j k k DeFunDiff j if abs k 2 disp Out of Interval return end dx abs k j dy abs FunDiff k n n 1 end y k end end function h FunDiff m h exp m 2 m end function dh DeFunDiff m dh m FunDiff m 2 exp m 2 1 end dx dy n y NewtonMethod 0 10 6 10 6 dx 3 2659e 07 dy 1 4802e 07 n 10 y 0 6529 Answer The point of intersection of f x and g x on the interval 2 2 is x 0 6529 Q4 2 package bisection public class Bis zz static double result 0 static int n 0 static int a 10 static int b 6 static double tol consec Math pow a b static double tol approx Math pow a b static void Bisection double a double b double mid a b 2 double y Math pow Math E Math pow mid 2 mid double ya Math pow Math E Math pow a 2 a double yb Math pow Math E Math pow b 2 b if ya yb 0 System out println change interval else if ya yb 0 if ya 0 result ya else result yb else if Math abs b a tol consec Math abs y tol approx result mid else if y 0 result mid else if y yb 0 b mid Bisection a b n else if y ya 0 a mid Bisection a b n public static void main String args TODO Auto generated method stub Bisection 2 2 System out println result System out println n n Answer 0 6529183387756348 3 package newton public class ND zz static double result 0 static int a 10 static int b 6 static double tol consec Math pow a b static double tol approx Math pow a b static int n 0 static double Newton double x double c Math pow x 2 double d Math pow Math E c double y d x double y1 2 x d 1 double x1 x y y1 if Math abs x 2 if Math abs y tol approx Math abs x1 x tol approx return result x else n return Newton x y y1 else System out println Out of internal return x public static void main String args TODO Auto generated method stub Newton 0 System out println result System out println n n Answer 0 6529186404370338