clear, close all;

%setup
h = 0.1; y0 = 1; N = 8/h; t = 0:h:8;
%pre-allocate arrays
y_ee = zeros(size(t)); y_ie = zeros(size(t)); y_mp = zeros(size(t));
%assign initial value
y_ee(1) = y0; y_ie(1) = y0; y_mp(1) = y0;

%numerical solutions
g = @(t) sin(t.^2); 
for ii = 1:N
    
    %explicit Euler
    y_ee(ii+1) = %complete here
    %implicit Euler
    y_ie(ii+1) = %complete here
    %implicit Midpoint Rule
    y_mp(ii+1) = %complete here
end

%reference solution with ode45
opts = odeset('AbsTol', 1e-10, 'RelTol', 1e-10);
[tref,yref] = ode45( @(t,y) sin(t.^2).*y, [0, 8], 1, opts);

%plot
plot(t,y_ee,'*-',t,y_ie,'*-',t,y_mp,'*-',tref, yref)
legend('ee','ie','mp', 'ref')