Question

MatLab code for Bisection and Newton Method to find root for f(k) = p(k)^3+2*(p(k)^2)-10 on interval [-1,2]. P(o)=1.5, P(1)=2.

Answer=
1.654249

Answer 1

%%Matlab code for finding root using Newton, Secant and Bisection method
clear all
close all

%Function for which root have to find
fun=@(x) x.^3+2.*x.^2-10;

%plotting of the function
xx=linspace(-1,2,1001);
yy=fun(xx);
plot(xx,yy)
xlabel('x')
ylabel('y')
title('f(x) vs x plot')

%displaying the function
fprintf('For the function\n')
disp(fun)

%Root using Newton method
x0=2; %Initial guess
maxit=1000; %maximum iteration
[root]=newton_method(fun,x0,maxit);
fprintf('Root using Newton method for initial guess %f is %2.15f.\n',x0,root);

%Root using Bisection method
x0=-1; x1=2; %Initial guess
maxit=1000; %maximum iteration
[root]=bisection_method(fun,x0,x1,maxit);
fprintf('Root using Bisection method for initial guess[%f,%f] is %2.15f.\n',x0,x1,root);

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%Matlab function for Bisection Method
function [root]=bisection_method(fun,x0,x1,maxit)
if fun(x0)<=0
    t=x0;
    x0=x1;
    x1=t;
end
%f(x1) should be positive
%f(x0) should be negative
k=10; count=0;
while k>eps
    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
root=xx(end);
end

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%Matlab function for Newton Method
function [root]=newton_method(fun,x0,maxit)
syms x
g1(x) =diff(fun,x);   %1st Derivative of this function
xx=x0;            %initial guess]
%Loop for all intial guesses
    n=eps; %error limit for close itteration
    for i=1:maxit
        x2=double(xx-(fun(xx)./g1(xx))); %Newton Raphson Formula
        cc=abs(fun(x2));                 %Error
        err(i)=cc;
        xx=x2;
        if cc<=n
            break
        end
      
    end
    root=xx;
end

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