pashin76,
<!DOCTYPE HTML>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.0/jquery.min.js"></script>
<script>
$(function(){
var t = $("#text"),data = Array(20).join("qwerty\n");
t.val(data + "\n").animate({scrollTop : t[0].scrollHeight - t[0].clientHeight},1500)
});
</script>
</head>
<body>
<textarea id="text" name="text" cols="20" rows="5"></textarea>
</body>
</html>