h=0.1 ; %timestep
Tmax=1;

tlist=linspace(0,Tmax,Tmax/h +1) ;
xlist=zeros(1,length(tlist));

%initialize
x0=1;
xlist(1)=x0;


for n=1:length(tlist)-1
    xlist(n+1)=xlist(n) + h/2*xlist(n) + h/2*(xlist(n) + h*xlist(n)) ;
end

figure
set(gca,'FontSize',16)
plot(tlist,xlist,'o','MarkerSize',16); hold on

tlistfine=linspace(0,Tmax,10000); 
plot(tlistfine,exp(tlistfine),'LineWidth',2);  %exact solution x=exp(t)

xlabel('t','Fontsize',20); ylabel('x(t)','Fontsize',20); 
legend('Heun Approx','Exact Solution')