Swing is based on the MVC pattern. Thus use a model. Changes to the model will automatically update the JComboBox
. For a deeper understanding in general read Swing Architecture Overview and for your case How to use ComboBoxes.
DefaultComboBoxModel favourites = new DefaultComboBoxModel();
favourites.addElement("Favourites");
favourites.addElement("-0.21 + 0.77");
favourites.addElement("-0.16 + -0.89");
jcb = new JComboBox(favourites);
in the other GUI method call
favourites.addElement("10 + 4");