Relationship Between Absolute Relative Approximate Error
Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages Description/Paper Instructions
Relationship Between Absolute Relative Approximate Error
Write a MATLAB function to calculate the 1st-order derivative of the function f(x) = sin(2x) at any given point correct within a specified significant digit using forward or central divided difference schemes. Your function should meet the following requirements: It should be named Numerical It should have four input arguments: 1) The first input argument is the point at which the first-order derivative is to be estimated; 2)
The second input argument is the number of correct significant digits specified; 3)
The third input argument is the starting step size; 4) The fourth input argument is either 1 or 2, where 1 means an FDD scheme should be used and 2 means a CDD scheme should be used. It should have three output arguments stored as a row vector: 1) The first output argument is the number of iterations performed; 2)
The second output argument is the final approximate first-order derivative; 3) The third output argument is the final absolute relative approximate error. The algorithm implemented in your function should start with the specified step size, keep halving it till you find the answer within a specified significant digit. Use a while-end loop for the procedure. You could initialize the relative approximate error to 1 at the beginning of the procedure. Create a flowchart first and demonstrate this portion of your code in your report. Your function should display the following: 1) At the beginning of your function, display on screen the divided difference scheme used for the calculation; 2)
In each iteration, your function should display on screen the current approximate value and the current absolute relative approximate error. Make sure your display has proper explanatory narrative. Show the screen display in your report. here is the tips with the command ———————————————————————————————————— % function to calculate the numerical differentiation with FDD/CD function = Numerical( ) % Initialization% iteration index I, initialized as 1% absolute relative approximate error, initialized as 1 to start the loop if % last input argument = 1, using
FDD% Display on screen which method is used dips();% Calculate the initial approximate with the initial step size% while-end loop% until the number of significant digits is achieved% recall the relationship between absolute relative approximate error and the number of significant digits (Ch01.02)while% Perform calculation using FDD% Screen display in each iterationfprintf(‘\n\nitration #%2d:\n’, )print(‘ die/dx at x = %.4e is %.4e\n’, , )print(‘ The absolute relative approximate error is %.4e\n’, )% Advance your loopendelseif % last input argument = 2, using
CDD% Display on screen which method is suedes (); % Calculate the initial approximate with the initial step size% while-end loop% until the number of significant digits is achieved% recall the relationship between absolute relative approximate error and the number of significant digits (Ch01.02) while% Perform calculation using
CDD% Screen display in each iterationfprintf(‘\n\nitration #%2d:\n’, print(‘ die/dx at x = %.4e is %.4e\n’, , )print(‘ The absolute relative approximate error is %.4e\n’, ) % Advance your looped% Final Outputfprintf(‘\n\n\the best approximate with %2d significant digits correct\n is %.4e after %2d iterations \n’, , , )print(‘The absolute relative approximate error is %g \n ‘, ) % Don’t forget to return your output variable end
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