%% Runge Kutta method %% 
%% Written for x'=f(x) with f(x)=-x and x(0)=x0

dt=.1;
x0=1;
t0=0;

endtime=1;
t=0:dt:endtime;

N=(endtime-t0)/dt;

x(1)=x0;


for n=1:N
   
    k1=(x(n)+exp(-x(n)))*dt;
    x2=x(n)+.5*k1
    k2=(x2+exp(-x2))*dt;
    x3=x(n)+.5*k2
    k3=(x3+exp(-x3))*dt;
    x4=x(n)+k3
    k4=(x4+exp(-x4))*dt;
    
    x(n+1)=x(n)+1/6*(k1+2*k2+2*k3+k4);
    
end

plot(t,x,'k')
hold on


%% END RUNGE KUTTA METHOD %%