Question

Hi, I need help doing this.

3. Use the bisection MATLAB program to estimate the roots of the function k(x) = x2 - 4, where x’s range is [-1, 3]. Include solutions for this method in the report.

Write a MATLAB program that uses the false-position method to estimate the roots of the function k(x) in problem#3. Include your m-file and solutions for this method in the report. In addition, submit your m-file separately.

Answer 1

Bisection Method in MATLAB

the code is as follows:

a=input('Enter function with right hand side zero:','s');

f=inline(a);

xl=input('Enter the first value of guess interval:') ;

xu=input('Enter the end value of guess interval:');

tol=input('Enter the allowed error:');

if f(xu)*f(xl)<0

else

    fprintf('The guess is incorrect! Enter new guesses\n');

    xl=input('Enter the first value of guess interval:\n') ;

    xu=input('Enter the end value of guess interval:\n');

end

for i=2:1000

xr=(xu+xl)/2;

if f(xu)*f(xr)<0

    xl=xr;

else

    xu=xr;

end

if f(xl)*f(xr)<0

    xu=xr;

else

    xl=xr;

end

xnew(1)=0;

xnew(i)=xr;

if abs((xnew(i)-xnew(i-1))/xnew(i))<tol,break,end

end

str = ['The required root of the equation is: ', num2str(xr), '']

For false position method the code is as follows:

clc

x0 = input('enter the value of x0 = ');

x1 = input('enter the value of x1 = ');

tolerance=input('inter the tolerance = ');

f =@(x) sin(2*pi*x)+ exp(1.2*x) + x - 2.5;

for i=0:inf

x2= x1 - (f(x1)* (x1-x0)/(f(x1)-f(x0)))

c = f(x2)

absolute_c= abs(c);

if absolute_c < tolerance

break

end

if f(x0)*c <0

x1=x2;

continue

else

x0=x2;

continue

end

end

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