Assignment 1 - Solving Nonlinear Equations; Due to October 30, 2007

• The function $h(x)=xsin(x)$ occurs in the study of undamped forced oscillations. Write a one complete program to solve $h(x)=1$ in [0,2] by:
  1. Halving the Interval (Bisection) Method
  2. The Method of False Position (regula falsi)
  3. Newton's Method
  4. Muller's method
  5. Fixed-point Iteration; $x=g(x)$ Method
• You can make use of the available matlab codes presented in the Hands-On sessions.
• Tabulate the actual error values as the following; (See Table 1. The number of iterations is not limited to or defined as 15.)
  

  Table 1: The Error Sequences

  	Bisection	Regula Falsi	Newton	Muller	Fixed-point
  n	$(x_n - r)$	$(x_n - r)$	$(x_n - r)$	$(x_n - r)$	$(x_n - r)$
  1
  2
  3
  4
  5
  6
  7
  8
  9
  10
  12
  13
  14
  15
  	Bisection	Regula Falsi	Newton	Muller	Fixed-point
  n	$f(x_n)$	$f(x_n)$	$f(x_n)$	$f(x_n)$	$f(x_n)$
  1
  2
  3
  4
  5
  6
  7
  8
  9
  10
  12
  13
  14
  15

  
  
• Plot the behaviours of the errors (use ratios) for the all cases. Compare and discuss the rate of convergence.