Creating a custom category teplate that lists child categories

Hi, I’m hoping that someone can help.

I have 5 parent categories for which I want to create separate category templates. On each template I want to list each post (title only) under it’s repective child category heading.

This is what I used (which obviously doesn’t work):

[please use the code button to mark any code – http://codex.wordpress.org/Forum_Welcome#Posting_Code ]

<div id="archive_list">
<h3>Grocery Savings</h3>
<?php get_posts('category=87'); ?>
<?php while (have_posts()): the_post(); ?>

<li><a href="”<?php">”><?php the_title(); ?></a></li>
<?php endwhile; ?>
</div>

Category ID 87 is the child category ID. I use this code for each child category.

Looks great, but is just listing the wrong things – it lists all the posts in the parent category without sorting as per child category.

Here’s what I’m aiming for: http://frugalandthriving.com.au/category/food-and-groceries/

Is it at all possible to create a custom list of links for just the posts in the child category?

My level of PHP is minimal at best, but I’m willing to learn :).

Thanks for any help in advance.