Computers And Technology High School

.. Write a MATLAB m-file that includes a MATLAB function to find the root xr of a function fx using the Bisection Your code must follow the following specifications: • Accept the function fx from the user. • Accept the initial bracket guess from the user. Default values (to be used. if no values are specified by the user) for the bracket are -1 and 1. • Accept stop criterion (approximate relative percent error, Ea) from the user. Default value is 0.001%. Accept the number of maximum number of iterations N (N = 200) from the user. Default value is N=50. This default vale is to be used if the user does not explicitly mention N. If N is reached and the stop criterion is not reached, print the message "Stop crtiterion not reached after N iterations. Exiting program." • If stop criterion is reached, print the value of the estimated root and the corresponding Ea (in %) with an appropriate message. • Test your program on an example function of your choice. Verify your answer against the solution obtained using another method ("roots" command or MS-Excel, etc.). Report both answers using a table. • Use clear and concise comments in your code so that a reader can easily understand your program. • Submit your program, a brief description of your approach, your observations, and conclusions. Note: Submit m-file as part of the PDF report and also separately as a .m file.

Answers

Answer 1

The given MATLAB code implements the Bisection method to find the root of a function within a specified stop criterion and maximum number of iterations, displaying the result or indicating if the stop criterion was not met.

The provided MATLAB m-file includes a function named "bisection_method" that takes the function "fx", initial bracket guess "bracket", stop criterion "Ea", and maximum number of iterations "N" as inputs. If the user does not provide any values, default values are used. The function calculates the root using the Bisection method by iteratively narrowing down the bracket until the stop criterion is met or the maximum number of iterations is reached.

The code checks the sign of the function at the endpoints of the bracket to determine if the root lies within the bracket. It then iteratively bisects the bracket and updates the endpoints based on the signs of the function at the new interval's endpoints. The process continues until the stop criterion is satisfied or the maximum number of iterations is reached.

If the stop criterion is met, the code displays the estimated root and the corresponding approximate relative percent error (Ea). If the stop criterion is not reached within the specified number of iterations, the code prints a message indicating that the stop criterion was not reached.

To verify the accuracy of the code, it can be tested on a chosen example function. The obtained root can be compared with the solution obtained using another method, such as the "roots" command in MATLAB or MS-Excel. The results can be reported in a table, displaying both the estimated root from the Bisection method and the root from the alternative method.

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