Question

Exercise 4: (Computer Problem) Write a function to implement the following al- gorithm and use your algorithm to find the solution of the equation et + sin x = 4 with initial bracket inteval (1,2). Print out the sequence of iterates, the errors ei, the error ratio ex+1/e; and ei+1/e? Is the convergence linear, super-linear, or/and quadratic? Given an interval [a,b] such that f(a) f(6) < 0 for i = 1,2,3,.. bf(a) – af(6) f(a) – f(b) if f(c) = 0, stop, end if f(a) f(c) < 0 CE b=c else a=C end end

Answer 1

ANSWER :

clear all
close all

%function for finding root
f=@(x) exp(x)+sin(x)-4;
a=1; b=2; tol=10^-10;

fprintf('function for the algorithm f(x)=')
disp(f)

fprintf('\t e_i \t e_i+1/e_i\t e_i+1/e_i^2\n')
i=0;fc=100; c=10;
while abs(fc)>tol
i=i+1;

fc=double(f(c));
err1=abs(fc);
c=double((b*f(a)-a*f(b))/(f(a)-f(b)));
if f(a)*f(c)<=0
b=c;
else
a=c;
end
err2=abs(f(c));
fprintf('\t%2.2e \t%2.2e \t%2.2e\n',err1,err2/err1,err2/err1^2)

end

OUT PUT :

function for the algorithm f(x)= C(x)exp(x)+sin(x)-4 ei e_i+1/e_i e_1+1/e i 2 2.20 +04 5.86e-06 2.661-10 1.29e-01 2.89e-01 2.24e+00 3.73e-02 2.88e-01 7.71e+00 1.07e-02 2.87e-01 2.68e+01 3.08e-03 2.87e-01 9.32e+01 8.85e-04 2.87e-01 3.25e+02 2.54e-04 2.87e-01 1.13e+03 7.29e-05 2.87e-01 3.94e+03 2.09e-05 2.87e-01 1.37e+04 6.01e-06 2.87e-01 4.78e +04 1.72e-06 2.87e-01 1.66e+05 4.952-07 2.87e-01 5.80e +05 1.42e-07 2.87e-01 2.02e+06 4.08e-08 2.87e-01 7.04e+06 1.17e-08 2.87e-01 2.45e+07