This paper presents novel implicit–explicit Runge–Kutta type methods for numerically
simulating partial integro-differential equations that arise when pricing options under jump …

Although the stabilization technique is favorable in designing unconditionally energy stable
or maximum-principle-preserving schemes for gradient flow systems, the induced time delay …

Splitting-based time integration approaches such as fractional step, alternating direction
implicit, operator splitting, and locally one dimensional methods partition the system of …

In recent years, stochastic partial differential equations (SPDEs) have become a well-studied
field in mathematics. With their increase in popularity, it becomes important to efficiently …

This paper is concerned with the adaptation of alternating direction implicit (ADI) time
discretization schemes for the numerical solution of partial integro-differential equations …

This work considers two boundary correction techniques to mitigate the reduction in the
temporal order of convergence in PDE sense (ie, when both the space and time resolutions …

For the numerical solution of parabolic problems with a linear diffusion term, linearly implicit
time integrators are considered. To reduce the cost on the linear algebra level, an …

Results on unconditional convergence in the maximum norm for ADI-type methods, such as
the Douglas method, applied to the time integration of parabolic problems are quite difficult …

This work considers space-discretised parabolic problems on a rectangular domain subject
to Dirichlet boundary conditions. For the time integration s-stage AMF-W-methods, which are …

Abstract Domain decomposition based time integrators allow the usage of parallel and
distributed hardware, making them well-suited for the temporal discretization of parabolic …