Matlab:Chapra , ROOTS [ Bracketing Method] Help needed.

  1. Hello guys can anyone help me solve this in matlab please ?


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  2. jcsd
  3. What are you having trouble with? Understanding the algorithm or implementing in Matlab?
     
  4. Thanks for your reply. Im having trouble implementing the code into matlab and getting correct answers. May you guide me through please ?
     
  5. If I had to find a zero of a simple function, say, x^2-3, using bisection, this is what I would write.

    Code (Text):

    % 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;
     
     
  6. 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
     
  7. 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.

    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.
     
  8. Help needed. ( Could you please help me to solve this problem in matlab? thanks

    (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.
     
  9. (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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