function Example1
% clc
% clear
close all

global lambda

% try different lambda = -1, 1, -10000,...
lambda = -1;

y0=1;
tmax=1;

% 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];
y=y0*exp(lambda*t);
%%%%%%%%%%%%%%%%%%


figure
plot(odeSolve.x, odeSolve.y,'o',t,y)
grid on
title('Example 1')
legend('numerical solution', 'analytical solution')

% see how many steps are needed for different lambda and different solvers (stiff/nonstiff)
fprintf('Number of integration steps: %g\n',length(odeSolve.y));

y_anal=y0*exp(lambda*odeSolve.x);
fprintf('Error: %g\n',norm(odeSolve.y-y_anal));

end


function dydt = f_dydt(t,y)
global lambda

dydt =  lambda*y;
end