leapfrog

clear all
clc
x(1) = 0.0; // initial position
v(1) = 2.0; // initial velocity
del_t = 0.2; // time increment
k = 0.1; // spring constant
m = 1.0; // mass
Tf = 100.0; // Final time
t = 0:del_t:Tf;
N = length(t);
v_hlf(1)=v(1)+(0.5*del_t*(-k/m)*x(1));
for j=2:N
    x(j)=x(j-1)+v_hlf(j-1)*del_t;
    v(j)=v_hlf(j-1)+0.5*(del_t*(-k/m)*x(j));
    v_hlf(j)=v(j-1)+0.5*(del_t*(-k/m)*x(j));
end
figure; plot(t, x);
grid on;