update a in index page without reloading

can someone direct me on how to do this, im using wordpress; Im using get_posts to retrieve the newest post and display the 2 previous post in a <li> tag on my index page

like below:

This a new post!
 -old post 1
 -old post 2

the desire i want is very simple, when a new post is being created, user’s dont have to reload the browser to update the index page.

Here’s my get_posts as above.

//DISPLAYS THE NEWEST POST
<?php
global $post;
$args = array( 'numberposts' => 1, 'category' => 1 );
$myposts = get_posts( $args );
foreach( $myposts as $post ) :	setup_postdata($post); ?>
	<div class="post"><h1><?php the_content(); ?></h1></div>

<?php endforeach; ?>	

//SHOWS 2 PREVIOUS POST
<?php
global $post;
$args = array( 'numberposts' => 2, 'offset'=> 1, 'category' => 1 );
$myposts = get_posts( $args );
foreach( $myposts as $post ) :	setup_postdata($post); ?>
	<li><?php echo get_excerpt(40); ?> - <a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
<?php endforeach; ?>