Bisection Method Table Generation Error - Array Indices Issue

I'm trying to create a MATLAB code that dynamically generates a table using the bisection method to estimate the drag coefficient of a bungee jumper. I have two files: `test.m` and `bisection_solver.m`. However, when I run the `test.m` script, I encounter an error that I can't seem to resolve. Here are the relevant code snippets:

File 1: test.m:

% Script 2
velocity_target = 46;   % Target velocity (m/s)
time = 9;               % Time of free fall (s)
g = 9.81;               % Acceleration due to gravity (m/s^2)
mass = 95;              % Mass of the bungee jumper (kg)

% Initial guesses and error criterion
xl = 0.2;
xu = 0.5;
error_criterion = 0.001;

% Initialize variables
Cd = (xl + xu) / 2; % Initial estimate of Cd
relative_error = 1; % Initialize with a value greater than the error criterion

% Define another mathematical expression as a function handle
expression = @(Cd) sqrt((mass * g) / Cd) * tanh(sqrt((Cd * g) / mass) * time);

% Call the bisection_solver function
[root, iterations] = bisection_solver(expression, xl, xu, error_criterion, Cd, relative_error);

fprintf('The root of the equation is %.6f after %d iterations.\n', root, iterations);

File 2: bisection_solver.m

function [root, iterations] = bisection_solver(expression, xl, xu, error_criterion, Cd, relative_error)

fprintf('Iteration\tLower Bound\tUpper Bound\tEstimated Cd\tRelative Error\n');

iteration = 0;

while relative_error > error_criterion
    
    iteration = iteration + 1;
    
    % Calculate the velocity using the current estimate of Cd
    velocity_estimated = expression(Cd);
    
    % Check if the estimated velocity is greater or smaller than the target
    if velocity_estimated > velocity_target
        xl = Cd; % Update the lower bound
        relative_error = abs((xl - xu) / xl);
    else
        xu = Cd; % Update the upper bound
        relative_error = abs((xu - xl) / xu);
    end
    
    if iteration > 1
        % Print the current iteration information
        fprintf('%d\t%.6f\t%.6f\t%.6f\t%.6f\n', iteration, xl, xu, Cd, relative_error);
    else 
        fprintf('%d\t%.6f\t%.6f\t%.6f\t--\n', iteration, xl, xu, Cd);
    end 
    
    % Calculate the new estimate of Cd using bisection
    Cd = (xl + xu) / 2;
    
end

fprintf('Hence, after the %d th iteration, the relative error is below %.2f%%.\n',iteration,  relative_error * 100);
fprintf('The final estimated drag coefficient is %.6f.\n', Cd);

end

When I run `test.m`, I get the following error message:

Iteration	Lower Bound	Upper Bound	Estimated Cd	Relative Error
Array indices must be positive integers or logical values.

Error in bisection_solver (line 13)
velocity_estimated = expression(Cd);

Expected Answer :

Iteration	Lower Bound	Upper Bound	Estimated Cd	Relative Error
1	0.350000	0.500000	0.350000	--
2	0.350000	0.425000	0.425000	0.176471
3	0.387500	0.425000	0.387500	0.096774
4	0.387500	0.406250	0.406250	0.046154
Hence, after the 4 th iteration, the relative error is below 4.62%.
The final estimated drag coefficient is 0.046154.

I'm not sure what's causing this error. Can someone help me identify and fix the issue so that I can successfully use the bisection method to estimate the drag coefficient and create the table?

Answer 1

[Dyuman Joshi]

You have

> not passed the variable velocity_target to the function

> not defined the output root in the function

Make the appropriate changes and the function should work