2 citations · 2 across the 6 of their papers we have counts for
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A simple predictor-corrector scheme without order reduction for advection-diffusion-reaction problems
Thi Tam Dang, Lukas Einkemmer, Alexander Ostermann
Treating diffusion and advection/reaction separately is an effective strategy for solving semilinear advection-diffusion-reaction equations. However, such an approach is prone to s…
Exponential integrators for parabolic problems with non-homogeneous boundary conditions
Carlos Arranz-Simón, Alexander Ostermann
Exponential Runge-Kutta methods are a well-established tool for the numerical integration of parabolic evolution equations. However, these schemes are typically developed under the…
Exponential Runge-Kutta methods for parabolic equations with state-dependent delay
Qiumei Huang, Alexander Ostermann, Gangfan Zhong
The aim of this paper is to construct and analyze exponential Runge-Kutta methods for the temporal discretization of a class of semilinear parabolic problems with arbitrary state-d…
Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators
Qiumei Huang, Alexander Ostermann, Gangfan Zhong
We derive error bounds for exponential Runge-Kutta discretizations of parabolic equations with nonsmooth initial data. Our analysis is carried out in a framework of abstract semili…
An initial-boundary corrected splitting method for diffusion-reaction problems
Thi Tam Dang, Lukas Einkemmer, Alexander Ostermann
Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order for Dirichlet boundary c…
On the convergence of split exponential integrators for semilinear parabolic problems
Marco Caliari, Fabio Cassini, Lukas Einkemmer +1
Splitting the exponential-like functions, which typically appear in exponential integrators, is attractive in many situations since it can dramatically reduce the computational…
Exponential Runge-Kutta methods of collocation type for parabolic equations with time-dependent delay
Qiumei Huang, Alexander Ostermann, Gangfan Zhong
In this paper, exponential Runge-Kutta methods of collocation type (ERKC) which were originally proposed in (Appl Numer Math 53:323-339, 2005) are extended to semilinear parabolic…
An initial-corrected splitting approach for convection-diffusion-reaction problems
Thi Tam Dang, Lukas Einkemmer, Alexander Ostermann
Splitting methods constitute a well-established class of numerical schemes for solving convection-diffusion-reaction problems. They have been shown to be effective in solving probl…