In MATLAB language please Write a function function [xroot, f root] = secant roo

Question

In MATLAB language please Write a function function [xroot, f root] = secant root (func, xl, xu) that takes a function func and returns the approximate root xroot as well as the function value froot at the approximate root; x1 and xu are the lower and upper bound of the secant interval, respectively. Secant root formula: x_root x_u - f(x_u) middot (x_1 - x_u)/f(x_1) - f(x_u), f_root = f(x_root) Test your function with the following input (define w(t), y(x) as anonymous functions in the workspace): y(x) = x^3, x_1 = -5, x_u = 5 w(t) = sin (t), t_1 = 2, t_u = 5 w(t) = sin (t), t_1 = 3, t_u = 4

Explanation / Answer

Main Function tto call the sacant function for all three problems:

%% MATLAB Code for sacant method
clc;
close all;
clear all;
disp('Solution for a :')
y=@(x) x^3;
[xroot, froot]= secantroot(y,-5,5)
disp('Solution for b :')
w=@(t) sin(t);
[xroot, froot]= secantroot(w,2,5)
disp('Solution for c :')
w=@(t) sin(t);
[xroot, froot]= secantroot(w,3,4)

%% Code of the function. Both main and function should be stored in same directory.

%% program strats here

function [xroot, froot]=secantroot(func,xl,xu)

xroot=xu-(func(xu)*(xl-xu)/(func(xl)-func(xu)));

froot=func(xroot);

maxerr=10^-4; flag = 1; maxiter = 100;

c = xroot;

while abs(froot) > maxerr

if func(xu)*func(c)<=0

xl = c;

elseif func(xl)*func(c)<=0

xu=c;

end

c= xu-(func(xu)*(xl-xu)/(func(xl)-func(xu)));

flag = flag + 1;

if(flag == maxiter)

break;

end

end

xroot = c;

froot=func(c);

Output :

Solution for a :

xroot =

0

froot =

0

Solution for b :

xroot =

3.1416

froot =

1.2246e-16

Solution for c :

xroot =

3.1416

froot =

1.2246e-16

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