# matlab:Chapra , ROOTS [ Bracketing Method] Help needed.

by uaeXuae
Tags: bracketing, matlabchapra, method, roots
 P: 54 Hello guys can anyone help me solve this in matlab please ?
 P: 212 What are you having trouble with? Understanding the algorithm or implementing in Matlab?
 P: 54 Thanks for your reply. Im having trouble implementing the code into matlab and getting correct answers. May you guide me through please ?
P: 212

## matlab:Chapra , ROOTS [ Bracketing Method] Help needed.

If I had to find a zero of a simple function, say, x^2-3, using bisection, this is what I would write.

% bisection.m
function bisection
% find root of x^2 - 3 on some interval

xa = 0;         xb = 10;        % search interval

for it = 1:20           % loop
xtest = xa + (xb-xa)/2;         % mid point of interval
fa = f(xa);                     % left-interval function value
fb = f(xb);                     % right-interval function value
ftest = f(xtest);               % mid-point function value
if sign(fa)*sign(ftest)<0       % if zero in left half
xb = xtest;                 %   take left half of interval
elseif sign(ftest)*sign(fb)<0   % if zero in right half
xa = xtest;                 %   take right half of interval
elseif ftest ==0                % if zero at mid-point
break                       %   this is the zero
else                            %
error('multiple roots or no root')  % may have no zero or multiple zeros
end
xit(it) = xtest;                % store mid-points
end
figure;plot(xit)                    % plot mid-points, should converge to the root

function y = f(x)                   % function we're finding the root of
y = x^2-3;
 P: 54 Thanx a lot. 2 questions: Q1) How do i input the equation ? Wherever it says "y = x^2-3" i replace it with the equation in the problem ? Q2) how do i get an error<0.00005
P: 212
 Quote by uaeXuae Q1) How do i input the equation ? Wherever it says "y = x^2-3" i replace it with the equation in the problem ?
Correct. Replace that with your equation. And you want to formulate the equation so you're finding a zero, so instead of finding x which solves f(x) = g(x), you want to find x which solves f(x) - g(x) = 0.

 Q2) how do i get an error<0.00005
You want to change the condition for the loop to terminate. One possible way would be to define a quantity x_error = f(x_test), and when abs(x_error) < tolerance, then x_test is sufficiently close to the root. In that case you could do a 'while x_error < tolerance' loop.
 P: 2 (1) Use a centered difference approximation O(h2) to estimate the second derivative of the function . (a) Perform the evaluation at x = 2 using step sizes of h = 0.2 and 0.1. Compare your estimates with the true value of the second derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion. (b) Write a Matlab program that evaluates the second derivative of the function (using a centered difference approximation O(h2)) on the interval [-4 , 4] with a step sizes of h = 0.2 and 0.1. Plot the second derivative of the function obtained by the centered difference method along with a graph obtained from a theoretical calculation. Submit the solution of part (a) as a hard copy. For part (b), submit a fully functional program to the blackboard, and submit a copy of the program and accompanying figures as a hardcopy.
 P: 2 (1) Use a centered difference approximation O(h2) to estimate the second derivative of the function . (a) Perform the evaluation at x = 2 using step sizes of h = 0.2 and 0.1. Compare your estimates with the true value of the second derivative. Interpret your results on the basis of the remainder term of the Taylor series expansion. (b) Write a Matlab program that evaluates the second derivative of the function (using a centered difference approximation O(h2)) on the interval [-4 , 4] with a step sizes of h = 0.2 and 0.1. Plot the second derivative of the function obtained by the centered difference method along with a graph obtained from a theoretical calculation. Submit the solution of part (a) as a hard copy. For part (b), submit a fully functional program to the blackboard, and submit a copy of the program and accompanying figures as a hardcopy.

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