use the secant method to determine resting membrane potential (e m) for j+ = 0.9 mm/min to an error tolerance of tol and an initial guess of x1se and x2se in the ghk equation in matlab in matlab

To use the secant method to determine the resting membrane potential (Em) for the given parameters in the GHK equation, you can follow these steps in MATLAB:

  1. Define the GHK equation as a function in MATLAB. Let's assume the function is called ghk_eqn and takes in the membrane potential (x) as the input parameter:
main.m
function result = ghk_eqn(x)
    % Given parameters
    j_plus = 0.9; % mm/min
    tol = 1e-6; % error tolerance

    % Rest of the GHK equation
    % Implement the rest of the equation using the given parameters
    % You can use variables such as j_plus, tol, etc. in this function

    % Calculate the result
    result = % Implement the GHK equation using the given parameters
end
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  1. Implement the secant method in MATLAB. Let's assume you have a function called secant_method which takes in the initial guesses (x1se and x2se) and the tolerance (tol) as input parameters:
main.m
function em = secant_method(x1se, x2se, tol)
    % Initialize variables
    max_iter = 100; % maximum number of iterations

    % Implement the secant method
    for i = 1:max_iter
        % Calculate the function values at current guesses
        f_x1 = ghk_eqn(x1se);
        f_x2 = ghk_eqn(x2se);
        
        % Calculate the next guess using the secant method formula
        x_next = % Implement the secant method formula
        
        % Check the error tolerance
        if abs(f_x2) < tol
            em = x2se; % Found the root within the tolerance
            return
        end
        
        % Update the guesses for the next iteration
        x1se = x2se;
        x2se = x_next;
    end

    % If the maximum number of iterations is reached, display an error message
    error('Secant method did not converge within the maximum number of iterations.');
end
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  1. Call the secant_method function with the initial guesses and the tolerance values to determine the resting membrane potential:
main.m
% Call the secant method function with the initial guesses and tolerance
x1se = % initial guess 1
x2se = % initial guess 2
tol = % error tolerance

em = secant_method(x1se, x2se, tol);

% Print the resulting resting membrane potential
disp(['Resting Membrane Potential (Em): ' num2str(em) ' mV']);
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Make sure you replace the placeholder values (% initial guess 1, % initial guess 2, % error tolerance) with the appropriate values for your specific problem.

Note: The secant method is an iterative approximation method, so the initial guesses should be chosen close to the expected solution to improve convergence.

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