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 …

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 …

A variable stepsize exponential multistep integrator, with contour integral approximation of
the operator-valued exponential functions, is proposed for solving semilinear parabolic …

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 …

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 …

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 …

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 …

The present work provides a comprehensive study of symmetric-conjugate operator splitting
methods in the context of linear parabolic problems and demonstrates their additional …

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 …

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 …