Splitting methods for differential equations
This overview is devoted to splitting methods, a class of numerical integrators intended for
differential equations that can be subdivided into different problems easier to solve than the …
differential equations that can be subdivided into different problems easier to solve than the …
Efficient time splitting schemes for the monodomain equation in cardiac electrophysiology
LP Lindner, T Gerach, T Jahnke… - International Journal …, 2023 - Wiley Online Library
Approximating the fast dynamics of depolarization waves in the human heart described by
the monodomain model is numerically challenging. Splitting methods for the PDE‐ODE …
the monodomain model is numerically challenging. Splitting methods for the PDE‐ODE …
A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data
A variable stepsize exponential multistep integrator, with contour integral approximation of
the operator-valued exponential functions, is proposed for solving semilinear parabolic …
the operator-valued exponential functions, is proposed for solving semilinear parabolic …
[HTML][HTML] Avoiding order reduction when integrating reaction–diffusion boundary value problems with exponential splitting methods
In this paper, we suggest a technique to avoid order reduction in time when integrating
reaction–diffusion boundary value problems under non-homogeneous boundary conditions …
reaction–diffusion boundary value problems under non-homogeneous boundary conditions …
Solving reaction-diffusion problems with explicit Runge–Kutta exponential methods without order reduction
In this paper a technique is given to recover the classical order of the method when explicit
exponential Runge–Kutta methods integrate reaction-diffusion problems. In the literature …
exponential Runge–Kutta methods integrate reaction-diffusion problems. In the literature …
How to avoid order reduction when Lawson methods integrate nonlinear initial boundary value problems
It is well known that Lawson methods suffer from a severe order reduction when integrating
initial boundary value problems where the solutions are not periodic in space or do not …
initial boundary value problems where the solutions are not periodic in space or do not …
Avoiding order reduction when integrating linear initial boundary value problems with exponential splitting methods
I Alonso-Mallo, B Cano… - IMA Journal of Numerical …, 2018 - academic.oup.com
It is well known the order reduction phenomenon which arises when exponential methods
are used to integrate time-dependent initial boundary value problems, so that the classical …
are used to integrate time-dependent initial boundary value problems, so that the classical …
Symmetric-conjugate splitting methods for evolution equations of parabolic type
The present work provides a comprehensive study of symmetric-conjugate operator splitting
methods in the context of linear parabolic problems and demonstrates their additional …
methods in the context of linear parabolic problems and demonstrates their additional …
Error estimates for a splitting integrator for abstract semilinear boundary coupled systems
We derive a numerical method, based on operator splitting, to abstract parabolic semilinear
boundary coupled systems. The method decouples the linear components that describe the …
boundary coupled systems. The method decouples the linear components that describe the …
Efficient boundary corrected Strang splitting
L Einkemmer, M Moccaldi, A Ostermann - Applied Mathematics and …, 2018 - Elsevier
Strang splitting is a well established tool for the numerical integration of evolution equations.
It allows the application of tailored integrators for different parts of the vector field. However …
It allows the application of tailored integrators for different parts of the vector field. However …