how can i improve this code to bacame better more

% matlab program for solving the bungee jumber problem using Eulers method
g=9.81;
m=80;
cd=0.25;
t0=0;
tend=20;
dt=0.5;
vi=0;
t=t0:dt:tend;
% the analytic solution
vel=sqrt(g*m/cd)*tanh(sqrt(g*cd/m)*t);
% the numrical solution
for ti=0:2:20
    v1=vi+(g-cd/m*vi.^2).*((ti+2)-ti)
    v2=v1+(g-cd/m*v1.^2).*((ti+2)-ti)
    v3=v2+(g-cd/m*v2.^2).*((ti+2)-ti)
    v4=v3+(g-cd/m*v3.^2).*((ti+2)-ti)
    v5=v4+(g-cd/m*v4.^2).*((ti+2)-ti)
    v6=v5+(g-cd/m*v5.^2).*((ti+2)-ti)
    v7=v6+(g-cd/m*v6.^2).*((ti+2)-ti)
    v8=v7+(g-cd/m*v7.^2).*((ti+2)-ti)
    v9=v8+(g-cd/m*v8.^2).*((ti+2)-ti)
    v10=v9+(c-cd/m*v9.^2).*((ti+2)-ti)
end
tt=[2 4 6 8 10 12 14 16 18 20]
v=[v1 v2 v3 v4 v5 v6 v7 v8 v9 v10]
% plotting of results
plot(t,vel)
hold on
plot(tt,v,'r')
grid
xlabel('time (s)')
ylabel('velocity (m/s)')
title('vilocity for the bungee jumber')
legend('analytical','numerical')

Answer 1

[Mark Sherstan]

Give this a try! Let me know if you have questions (I have commented my changes).

% matlab program for solving the bungee jumber problem using Eulers method
g=9.81;
m=80;
cd=0.25;
t0=0;
tend=20;
dt=0.5;
vi=0;
t=t0:dt:tend;

% the analytic solution
vel=sqrt(g*m/cd)*tanh(sqrt(g*cd/m)*t);

% Pre allocate memory for faster run times
v = zeros(11,1);
tt = zeros(11,1);
count = 2;

% Loop through your calculations knowing that initial conditions are zero
for ti = 2:2:20
    v(count) = v(count-1) + (g-cd/m*v(count-1).^2).*((ti+2)-ti);
    tt(count) = ti;
    count = count + 1;
end

% plotting of results
plot(t,vel)
hold on
plot(tt,v','r')
grid
xlabel('time (s)')
ylabel('velocity (m/s)')
title('velocity for the bungee jumber')
legend('analytical','numerical')