The forward-Euler method is also called explicit method because the calculation of every flow and every source term of the equation to be solved is based on the old time level *t*_{n}. The only variable at the time *t*_{n+1} is the variable in the vertex *i*. The variable is thus calculated without reference to any values of adjacent vertices (spatial derivatives), i.e. explicitly. Additional conditions have to be made for the time-step (time increment ) in order to achieve stable solutions with this method. These conditions are defined in dependency of the Peclet number. The time-step method used in RMA2 is an explicit method like as described above.

The backward-Euler method is an implicit method because the spatial derivatives, for example, are based only on the values of (adjacent) vertices of the current time level *t*_{n+1}. The implicit method has no restrictions concerning the width of time-steps and its effect on the stability of the calculation as opposed to the explicit method. On the other hand, it is an iterative method, which means a higher numerical effort for the individual time-steps.

More detailed explanations concerning the solving of unsteady problems can be found in [*1]* *among others*.*