[SOLVED] CSE218-Secant & False Position Method

Description

1. ln (1+x) function can be expanded  using Taylor series and the expanded series is given below.

Now write a single program to perform the following tasks:

1. Take the value of x and iteration (number of terms) number n and return the approximated value of ln(1+x).                                                          [2]

1. Plot the ln (1+x)  function for the interval -1<x<=1 with step size 0.1 using the built-in log (x) function.                                                             [3]
2. In the same plot (one plot for 1(a) and 1(b)) show five approximated functions for the same interval using different number of terms (1, 3, 5, 20, 50).                                                                    [5]

1. Draw another plot showing the relative approx. error for each iteration while determining the value of ln(1.5) upto 50 terms.                                  [5]

2. In a chemical engineering process, water vapor (H₂O) is heated to sufficiently high temperatures that a significant portion of the water dissociates, or splits apart, to form oxygen (O₂) and hydrogen (H₂):

H₂O←→ H₂ + 1/2 O₂

If it is assumed that this is the only reaction involved, the mole fraction  x of H₂O that dissociates can be represented by

K=x/(1-x) *√(2p_t/(2+x))

where K is the reaction’s equilibrium constant and p_t is the total pressure of the mixture. If p_t= 3 atm and K = 0.05, determine the value of x that satisfies given equation.

Write a single program which does the following:

• Uses graphical model to estimate the value. [5]
• Uses Secant method and False Position method to estimate the value for ε_s=0.5%. Report the number of iterations for each method  while achieving the expected result.                                                              [7.5+7.5=15]

Secant Method and False Position method should be implemented as separate functions following the prototype given below:

• Secant method (function , 1^st initial guess, 2^nd initial guess, expected relative approximation error, max iteration)

• False Position method (function , lower bound of the bracket, upper bound of the bracket, expected relative approximation error, max iteration)

Please note that following the prototypes is mandatory.