Galerkin/Runge-Kutta discretizations for semilinear parabolic equations
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
Numerical solution of partial differential equations
Numerical solution of partial differential equations
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
Maximum Norm Analysis of Completely Discrete Finite Element Methods for Parabolic Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
The Trotter-Kato theorem and approximation of PDEs
Mathematics of Computation
Explicit single step methods with optimal order of convergence for partial differential equations
Applied Numerical Mathematics
Rational methods with optimal order of convergence for partial differential equations
Applied Numerical Mathematics
Optimal orders of convergence for Runge-Kutta methods and linear, initial boundary value problems
Applied Numerical Mathematics
Accelerating the convergence of spectral deferred correction methods
Journal of Computational Physics
Arbitrary order Krylov deferred correction methods for differential algebraic equations
Journal of Computational Physics
On Time Staggering for Wave Equations
Journal of Scientific Computing
Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems
Journal of Computational Physics
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A new strategy to avoid the order reduction of Runge-Kutta methods when integrating linear, autonomous, nonhomogeneous initial boundary value problems is presented. The solution is decomposed into two parts. One of them can be computed directly in terms of the data and the other satisfies an initial value problem without any order reduction. A numerical illustration is given. This idea applies to practical problems, where spatial discretization is also required, leading to the full order both in space and time.