leap frog integration in matlab

main.m
% Define initial conditions
t0 = 0;
tf = 10; % final time
dt = 0.01; % time step
t = t0:dt:tf; % time array

% Initialize arrays
N = length(t);
x = zeros(1, N);
v = zeros(1, N);

% Define initial position and velocity
x(1) = 1;
v(1) = 0;

% Perform leapfrog integration
for i = 2:N
    % Update position
    x(i) = x(i-1) + v(i-1)*dt;
    
    % Update velocity
    if i < N
        v(i) = v(i-1) + (some_force(x, v, i-1) * dt); % Here, some_force is the function for the force at a given position
    end
end

% Plot results
plot(t, x);
xlabel('Time');
ylabel('Position');
title('Leapfrog Integration Result');

function force = some_force(x, v, i)
    % Function to calculate force at a given position
    force = -x(i); % Example force function, you should replace this with your actual force equation
end
809 chars
37 lines