clear all;
close all;
epsilon=0.00001;
Delta_t=1;
t=0:Delta_t:2.0/epsilon;
%Preallocating memory
x=zeros(size(t));
x(1)=epsilon;
for n=1:length(t)-1
x(n+1)=x(n)+f(t(n),x(n))*Delta_t;
end
%
%Computing Matlab solution
%
[tmat,xmat]=ode23(@f,[0 2/epsilon],epsilon);
plot(t,x,’ko-‘,tmat,xmat,’bs-‘)
hold on
xlabel(‘t’);
ylabel(‘x’);
legend(‘Explicit Euler’,’MATLAB’);
function dxdt=f(t,x)
dxdt=x*(x-x^2);
end