EE342.01: MATLAB M-FILE FOR COMPARING EXACT SOLUTION OF DIFFERENTIAL EQUATION WITH NUMERICAL SOLUTION

%
%  Filename:  example6.m
%
%  Description:  M-file to compare exact and numerical solutions
%                of a CLTI differential equation.
%

clear;                                  % clear matlab memory

tmax = 10.0;                            % amount of time to run simulation

t = 0:0.01:tmax;                        % CT time values
y = 0.5 + 1.26*exp(-0.75*t).*cos(1.2*t + 1.98); % Exact Solution

plot(t,y); xlabel('t ');           % Plot exact (CT) solution
ylabel('y(t)'); title('Solutions to Differential Equation');
hold on;

T = 0.2;                                % Sample time
N = tmax/T;                             % Final DT value
yprev2 = 0;                             % y[0]
yprev1 = -T;                            % y[1]

nvec = [0 1];                           % Store ICs for plotting
yvec = [yprev2 yprev1];

for n = 2:N,

  y = (2 - 3*T/2)*yprev1 + (3*T/2 - 2*T*T - 1)*yprev2 + T*T;  % Diff. Eqn.
  yprev2 = yprev1;
  yprev1 = y;

  nvec(n+1) = n;
  yvec(n+1) = y;

end;

plot(nvec*T, yvec, 'o');
hold off;

gtext('--- y(t); ooo y[n] w/T=0.2');