solve the ghk equation using the above constants using the bisection method to an error tolerance of tol and an initial guess of x1bi and x2bi. in matlab

To solve the GHK (Goldman–Hodgkin–Katz) equation using the bisection method in MATLAB, you can follow these steps:

  1. Define a function that represents the GHK equation. Let's call it ghk_eq.
main.m
function result = ghk_eq(x)
    % Constants
    R = 8.314;
    T = 273.15 + 25;
    F = 96485;
    P_K = 10^-2;
    P_Na = 10^-2;
    P_Cl = 10^-2;
    C_Kin = 10^-2;
    C_Nain = 145;
    C_Cl = 110;
    V = -0.070;

    % GHK equation
    result = x - (P_K * C_Kin + P_Na * C_Nain * exp(-x * F / (R * T)) + P_Cl * C_Cl) / (P_K + P_Na * exp(-x * F / (R * T)) + P_Cl);
end
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  1. Implement the bisection method in MATLAB. Let's call it bisection_method.
main.m
function result = bisection_method(tol, x1bi, x2bi)
    % Bisection method implementation
    while abs(x2bi - x1bi) > tol
        xbi = (x1bi + x2bi) / 2;
        if ghk_eq(xbi) == 0
            break;
        elseif ghk_eq(xbi) * ghk_eq(x1bi) < 0
            x2bi = xbi;
        else
            x1bi = xbi;
        end
    end
    result = xbi;
end
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  1. Call the bisection_method function with the desired error tolerance (tol) and the initial guesses for x1bi and x2bi.
main.m
tol = 1e-6;
x1bi = -0.100;
x2bi = 0.100;

solution = bisection_method(tol, x1bi, x2bi);
disp(solution);
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This will compute the solution to the GHK equation using the bisection method in MATLAB, given the specified error tolerance and initial guesses.

Please note that the code assumes you have defined the ghk_eq and bisection_method functions in the same MATLAB file or in separate files in the same folder.

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