You are updating the time t and y values, they are of size 1x1 so the final plot will only show you a point, you have to append to the time vector and y vector and then use it to plot, here is your own modified code, I have defined two empty arrays t1 and y1 and then appending to them inside the while loop.
dy=@(t,y) -(0.1/10^(1/2))^2*(2*9.8*y)^(1/2); %ODE
t=0; %initial t
y=2*sqrt(10); %Initial y
h=0.05; %Half step
a=1136; %approximate value
t1=[];y1=[]; %%%% added line %%%%%%%
while a-t >= -10^(-5) %loop until given approximate value
dty = dy(t,y);
tn = t+h; %new t value
yp = y + h*dty; %placeholder y value
dtnyp = dy(tn,yp);
yn = y + (h/2)*(dty + dtnyp); %new y value
t = tn; %update t value
y = yn; %update y value
t1=[t1,t]; %%% append to time vector
y1=[y1,y]; %%% append to ouptput y vector
end
figure ;
grid on ;
title ('Solution using Euler Imrpoved method')
plot(t1, y1, 'b','lineWidth',1.5) %% the vectors accumulated are used in plotting
I hope this answers your query, please accept the answer if it does
Thank you
