function Example2
% clc
% clear
close all

y0=[1;0]; %[x;y]
tmax=2*pi;

% try different ode solvers - ode45, ode23, ode15s
odeSolve=ode45(@f_dydt,[0,tmax],y0); %[uc, i]

%%%%%%%%% analytic solution %%%%%%%%%
dt=1000;
t=[0:tmax/dt:tmax];
x=sin(t);
y=cos(t);
%%%%%%%%%%%%%%%%%%


figure
plot(odeSolve.x, odeSolve.y,'o',t,x,t,y)
grid on
title('Example 2')
legend('numerical solution', 'analytical solution')

fprintf('Number of integration steps: %g\n',length(odeSolve.y));

x_anal=sin(odeSolve.x);
y_anal=cos(odeSolve.x);
fprintf('Error: %g\n',norm(odeSolve.y-[y_anal;x_anal]));

end


function dydt = f_dydt(t,y)
dydt = zeros(2,1);    % a column vector
dydt(1) =  -y(2);
dydt(2) =  y(1);
end