solve the dae below dz dt = −2z + y 2 5 = 2z − 100 log(y) with the initial conditions z(0) = 2 and y(0) = 0.99005. in matlab

To solve the given DAE (Differential-Algebraic Equation) using MATLAB, you can use the ode15i solver which is designed specifically for solving DAEs. Here's how you can do it:

main.m
% Define the system of DAEs
f = @(t, Z, Zd) [Zd(1) + 2*Z(1) - Z(2)^2/5;
                 Zd(2) - 2*Z(1) + 100*log(Z(2))];

tspan = [0 1]; % Time span
Z0 = [2; 0.99005]; % Initial conditions for z and y

% Solve the DAE using ode15i
options = odeset('RelTol', 1e-6);
[t, Z] = ode15i(f, tspan, Z0, options);

% Extract the solutions
z = Z(:, 1);
y = Z(:, 2);

% Plot the solutions
plot(t, z, 'b', t, y, 'r');
legend('z(t)', 'y(t)');
xlabel('Time');
ylabel('Solution');
title('Solutions of the DAE');

% Display the final values of z and y
final_z = z(end);
final_y = y(end);
fprintf('Final value of z: %f\n', final_z);
fprintf('Final value of y: %f\n', final_y);
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Make sure to replace the equations in the f anonymous function with your actual equations. The tspan variable represents the time span for which you want to solve the DAE. Adjust it accordingly.

The options variable sets the relative tolerance for the solver. You can adjust this value as per your requirement.

The solutions for z and y will be stored in the z and y variables, respectively. The code also plots the solutions over the given time span and displays the final values of z and y.

Note: It's important to note that depending on the nature of your DAE, ode15i might not converge to a solution or produce accurate results. In such cases, you might need to try other solvers or employ specialized techniques.