There is more than one way to do that:
$this->{$methodName}($arg1, $arg2, $arg3);
$this->$methodName($arg1, $arg2, $arg3);
call_user_func_array(array($this, $methodName), array($arg1, $arg2, $arg3));
You may even use the reflection api http://php.net/manual/en/class.reflection.php