In this work we present a class of high order unconditionally strong stability preserving (SSP) implicit two-derivative Runge--Kutta schemes and SSP implicit-explicit (IMEX) multi-derivative where the time-step restriction is independent stiff term. The unconditional property for method $p>2$ unique among methods depends on backward-in-time assumption derivative operator. We show that backward ...

Recent studies on knowledge base completion, the task of recovering missing relationships based on recorded relations, demonstrate the importance of learning embeddings from multi-step relations. However, due to the size of knowledge bases, learning multi-step relations directly on top of observed triplets could be costly. Hence, a manually designed procedure is often used when training the mod...

Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties–in any norm or seminorm—of the spatial discretization coupled with first order Euler time stepping. This paper describes th...

Popular approaches for solving the shallow water equations (SWE) for climate modeling are explicit and semi-implicit methods, both have certain constraints on the time step size. In this paper, we propose and study a fully implicit method which imposes no limit on the time step size, but requires the solution of a large sparse nonlinear system of equations at every time step. The focus of the p...

The temporal discretization scheme is one important ingredient of efficient simulator for twophase flow in the fractured porous media. The application of single-scale temporal scheme is restricted by the rapid changes of the pressure and saturation in the fractured system with capillarity. In this paper, we propose a multi-scale time splitting strategy to simulate multi-scale multi-physics proc...

In a previous study [21], a class of efficient semi-implicit schemes was developed for stiff reaction-diffusion systems. This method which treats linear diffusion terms exactly and nonlinear reaction terms implicitly has excellent stability properties, and its second-order version, with a name IIF2, is linearly unconditionally stable. In this paper, we present another linearly unconditionally s...

Implicit-explicit (IMEX) linear multistep methods are popular techniques for solving partial differential equations (PDEs) with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily impleme...

This paper investigates the expected benefits of the implicit time integration scheme in the solution of jointed rock problems. Discontinuous Deformation Analyses (DDA) exploits the unconditional stability of the implicit time integration scheme, and allows the time step size of the solution to be much larger than the critical time step size dictated by the stability requirement of the explicit...

This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule heating equations. We present optimal error estimates of the semi-implicit Euler scheme in both the L norm and the H norm without any time-step restriction. Theo...