Spectral/Rosenbrock discretizations without order reduction for linear parabolic problems Original Research Article

The order reduction phenomenon occurs when a Rosenbrock method is used together with the method of lines for the full discretization of an initial boundary value problem. This phenomenon can be avoided with a right choice of the boundary values of the intermediate stages. This fact is proved for time discretizations of abstract initial boundary value problems with variable stepsize. These results are applied for the study of full discretizations of parabolic problems by using spectral methods for the spatial discretization. Some numerical examples confirm that the optimal order is achieved.