Question

Write a script that uses the function below to find root brackets for ?(?) = cos(e^x) + sin(?), between ? = 0 ??? ? = ? with ns=100. Plot the output by first plotting the function and then plotting ‘*’ at each bracket point (on the x-axis). You may either give the plot() function two sets of inputs, or you can use hold on ... hold off to add plots to your figure.

function xb = incsearchv(func,xmin,xmax,ns)

Answer 1

clear all
close all
%function for which root have to find
func=@(x) cos(exp(x))+sin(x);
fprintf('function for which root have to find f(x)=')
disp(func)
%upper and lower limit
x0=0; x1=pi;
xx=linspace(x0,x1,1000);
yy=func(xx);
plot(xx,yy)
xlabel('x')
ylabel('f(x)')
title('x vs. f(x) plot')
[root]=incsearchv(func,x0,x1,100);
hold on
plot(root,func(root),'r*')

%Matlab function for Bisection Method
function [root]=incsearchv(fun,x0,x1,maxit)
if fun(x0)<=0
    t=x0;
    x0=x1;
    x1=t;
end
fprintf('\nRoot using Bisection method\n')
%f(x1) should be positive
%f(x0) should be negative
k=10; count=0;
while k>5*10^-10
    count=count+1;
    xx(count)=(x0+x1)/2;
    mm=double(fun(xx(count)));
    if mm>=0
        x0=xx(count);
    else
        x1=xx(count);
    end
    err(count)=abs(fun(x1));
    k=abs(fun(x1));
    if count>=maxit
        break
      
    end
    %
end
fprintf('\tAfter %d iteration root using Bisection method is %f\n',count,xx(count))
root=xx(end);
end

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