Avoiding order reduction of fractional step Runge–Kutta discretizations for linear time dependent coefficient parabolic problems Original Research Article

In this paper we study the order reduction, caused by the presence of time dependent boundary conditions, in the integration of linear parabolic problems whose coefficients may depend on time by means of fractional step Runge–Kutta methods. This kind of methods includes most of classical splitting, alternating direction or fractional step schemes, as well as new methods of the same types but with higher orders of accuracy. It is proven that such order reduction can be avoided by modifying suitably the commonly chosen boundary values for the calculus of the internal stages (or the intermediate fractionary steps) of the method. Some numerical examples are presented in order to show the practical implications of the theoretical achievements.