Question

Problem 3: (a) Fine the root for the equation given below using the Bisection and Newton-Raphson Numerical Methods (Assume initial value) using C++Programming anguage or any other programming angua ge: x6+5r5 x*e3 - cos(2x 0.3465) 20 0 Use tolerance 0.0001 (b) Find the first five iterations for both solution methods using hand calculation. Note: Show all work done and add your answers with the homework Show Flow Chart for Bisection and Newton-Raphson Methods for Proramming. Note: Yur amwer Som the programming , to be " " the hmework. needs to be shown in the homework

Answer 1

Matlab code for Bisection method:

eqn= @(x) (x^6)+(5*x^5)+(x^4*exp(3*x))-cos (2*x+0.3465)-20;

answer = p(eqn,0,1)

function p = bisection(f,a,b)
% f - function

% a- guess 1

% b- guess 2
if f(a)*f(b)>0
disp('change guess')
else
p = (a + b)/2;
err = abs(f(p));
while err > 1e-7
if f(a)*f(p)<0
b = p;
else
a = p;
end
p = (a + b)/2;
err = abs(f(p));
end
end

Matlab code for Newton-Raphson method:

syms x;
f=(x^6)+(5*x^5)+(x^4*exp(3*x))-cos (2*x+0.3465)-20; %Enter the Function here
g=diff(f); %The Derivative of the Function
epsilon = 0.0001;
x0 = input('Enter the intial approximation:');
for i=1:100
f0=vpa(subs(f,x,x0)); %Calculating the value of function at x0
f0_der=vpa(subs(g,x,x0)); %Calculating the value of function derivative at x0
y=x0-f0/f0_der; % The Formula
err=abs(y-x0);
if err<epsilon %checking the amount of error at each iteration
break
end
x0=y;
end
y = y - rem(y,10^-n); %Displaying upto required decimal places
fprintf('The Root is : %f \n',y);
fprintf('No. of Iterations : %d\n',i);