Question

1. (30 points) Write a MATLAB code to perform the Secant method of root finding. Write the code to output the table used in class showing the iteration, root estimate r,, function value at the root estimate f(r,), and the approximate error. Show that the code works by using it to re-solve Homework Assignment II Problem 2c. Which asked you to find the positive root of f(r) r,1.0 and 6 10-6, have the code iterate until the approximate error is less than 1% . 5-3r-4 using the mass of each rod is listed below Jaseent

Answer 1

The Matlab program for above problem is:::

O - D Stack: Base fx : % 9 9 - A - 1.0 + = 1.1 x * Modeified Secant clc clear all N=100; no. of iteration err=0.01; } Accuracy of result f=@(x) (5*x^2-3*x-4); wanted eg. to be solved x1=input('Initial Guess =....'); delta=input ('perturbation Fraction=.....'); xx (1)=x1; modified secant law for i=2:N x2=x1-(f(x1) *delta*xl) / (f(x1+delta*xl)-f(x1)); x1=x2; xx(i)=x2; iiri; Number of iteration Err=abs(xx(i)-xx (i-1)); if Err<err, break; end convergance condition Мнт eal_root=fzero (f, 1); fprintf('the root is Verification from built in function f \n with accuracy }f \n no. of iteration f In the real root is f', x2, Err, ii, real_root)

The Solution in command window:

+ Dax Command Window Initial Guess =....1 perturbation Fraction=.....10^-6 the root is 1.243399 with accuracy 0.000908 no. of iteration 4.000000 fx the real root is 1.243398>>