% =========================================================================
%   Praktikum MATLAB/Simulink I
%   Technische Universität Darmstadt
%   IAT, FG rtm (Prof. Dr.-Ing. U. Konigorski)
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%                       Technische Universität Darmstadt
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% =========================================================================

% Versuch 3.1
% Versuchsdurchführung 3.1.6 Vergleich der Berechnungsmethoden

%%  Definition der Konstanten


%% Analytische Lösung (Teil I)
T = 15; %max Zeit
[x_ana_1, t_ana_1] = AnalytischeLoesung(omega, Parameter, T(1), P1, P2);

%% Numerische Lösung (Teil II)
x0 = [0 0].'; %Anfangsbedingungen
T = 15; %max Zeit
[x_num_11, t_num_11] = NumerischeLoesung(T, x0, 1);
[x_num_21, t_num_21] = NumerischeLoesung(T, x0, 2);

%% Diskrete Lösung (Teil III)
N = 30; %30 Schritte
T0 = 0.5; % Definition der Schrittweiten
[x_dis_1, t_dis_1] = DiskreteLoesung(Parameter, omega, N, T0);

%% Plotten der Ergebnisse
figure()
plot(t_ana_1, x_ana_1, '--', t_dis_1, x_dis_1, ':', ...
        t_num_11, x_num_11, ':', t_num_21, x_num_21, '--', 'linewidth', 2);
legend('Analytisch', 'Diskret', ...
            'Numerisch; Explizit', 'Numerisch; Implizit');
xlabel('t / s');
ylabel('x(t) / m');
grid on

