Avoiding order reduction of Runge-Kutta discretizations for linear time-dependent parabolic problems
A technique is developed to avoid order reduction when discretizing linear parabolic problems with time dependent operator using Runge-Kutta methods in time and standard schemes in space. The authors improve the time convergence rate for parabolic initial boundary value problems where the operator may depend on time although the boundary operator is still time-independent. It is observed that the derivation of an improved rate in time has only been studied for time- dependent coefficients by \textit{S. L. Keeling} [Math. Comput. 52, No. 186, 561--586 (1989; Zbl 0669.65084)], where an extrapolation technique is used.
scientific article; zbMATH DE number 2081526