9 papers
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…
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…
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 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…
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…