Stability and convergence at the PDE/stiff ODE interface
Applied Numerical Mathematics - Recent Theoretical Results in Numerical Ordinary Differential Equations
Galerkin/Runge-Kutta discretizations for semilinear parabolic equations
SIAM Journal on Numerical Analysis
Rosenbrock methods for partial differential equations and fractional orders of convergence
SIAM Journal on Numerical Analysis
A stability result for sectorial operators in branch spaces
SIAM Journal on Numerical Analysis
On the stability of variable stepsize rational approximations of holomorphic semigroups
Mathematics of Computation
Runge-Kutta approximation of quasi-linear parabolic equations
Mathematics of Computation
Interior estimates for time discretizations of parabolic equations
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Explicit single step methods with optimal order of convergence for partial differential equations
Applied Numerical Mathematics
Runge-Kutta methods for linear ordinary differential equations
Applied Numerical Mathematics
Rational methods with optimal order of convergence for partial differential equations
Applied Numerical Mathematics
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Journal of Computational and Applied Mathematics
Construction of a multirate RODAS method for stiff ODEs
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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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.