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

main.m
function f = ghk_equation(E_m, j_plus)
    % Constants
    R = 8.314;   % Gas constant (J/(mol K))
    T = 310;     % Temperature (K)
    F = 96485;   % Faraday's constant (C/mol)
    P_K = 1e-6;  % Permeability of potassium (m/s)
    P_Na = 3e-7; % Permeability of sodium (m/s)
    P_Cl = 8e-8; % Permeability of chloride (m/s)
    C_in = 150;  % Concentration inside the membrane (mM)
    C_out = 15;  % Concentration outside the membrane (mM)

    % GHK equation
    f = P_K*C_out*(exp(-F*E_m/(R*T))-exp(-F*E_m/(R*T)))...
        + P_Na*C_out*(exp(-F*E_m/(R*T))-exp(-F*E_m/(R*T)))...
        - P_Cl*C_in*(exp(-F*E_m/(R*T))-exp(-F*E_m/(R*T)))...
        - j_plus;
end
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main.m
x1 = x1se; % Initial guess 1
x2 = x2se; % Initial guess 2
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main.m
max_iterations = 100;    % Maximum number of iterations
tol = tol;               % Error tolerance
iteration = 0;
error = tol+1;

while error > tol && iteration < max_iterations
    iteration = iteration + 1;

    % Evaluate the function at x1 and x2
    f_x1 = ghk_equation(x1, j_plus);
    f_x2 = ghk_equation(x2, j_plus);

    % Compute the new estimate using the secant method
    x3 = x2 - f_x2*(x2 - x1)/(f_x2 - f_x1);

    % Update the estimates
    x1 = x2;
    x2 = x3;

    % Compute the error
    error = abs(x2 - x1);
end

% The final estimate is the resting membrane potential (E_m)
E_m = x2;
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main.m
x1se = 0;   % Initial guess 1
x2se = -70; % Initial guess 2
tol = 1e-6; % Error tolerance

E_m = secant_method_ghk(x1se, x2se, tol, j_plus);
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