Balance&characteristic finite difference schemes for the equations of the parabolic type

A new numerical algorithm for solving parabolic equations by means of balance&characteristic difference schemes is proposed. The balance&characteristic schemes are combining the advantages of conservative and characteristic schemes. The main advantage of the new algorithm is that it is explicit and is implemented on the most compact computational template in one space-time computational cell. It scales perfectly and is extremely economical in software systems that implement the CABARET scheme because it uses the existing data structure there.